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An Experimental Study of Search in Global Social Networks
Abstract
We report on a global social-search experiment in which more than 60,000 e-mail users attempted to reach one of 18 target
persons in 13 countries by forwarding messages to acquaintances. We find that successful social search is conducted primarily
through intermediate to weak strength ties, does not require highly connected “hubs” to succeed, and, in contrast to unsuccessful
social search, disproportionately relies on professional relationships. By accounting for the attrition of message chains,
we estimate that social searches can reach their targets in a median of five to seven steps, depending on the separation of
source and target, although small variations in chain lengths and participation rates generate large differences in target
reachability. We conclude that although global social networks are, in principle, searchable, actual success depends sensitively
on individual incentives.
... In the 1960's and 70's, participants in small world experiments successfully found paths connecting individuals from Nebraska to Boston and from Los Angeles to New York . In 2002, 60,000 individuals were able to repeat the experiment using email chains with an average of 4.1 links to bridge continents (Dodds et al., 2003). ...
... We will tie these models to the small world and reverse small world experiments by simulating on real world networks the strategies people have reported using and comparing the success of these strategies with the degree to which the networks conform to a theoretically searchable structure. Note that we are not examining here what small world participants actually do, as this has been the subject of extensive work Bernard, 1978, 1979;Lundberg, 1975;Milgram, 1967;Travers and Milgram, 1969;Dodds et al., 2003). Rather, we are taking the strategies that participants have reported using, and are testing, in two experiments, when these strategies really can be used successfully and why. ...
... Bernard et al. (1982) found that contacts were chosen because they "knew a lot of people" only 7 percent of the time. Similarly, Dodds et al. (2003) found that individuals in successful chains were far less likely than those in incomplete chains to choose recipients based on their degree (1.6 versus 8.2%). ...
We address the question of how participants in a small world experiment are able to find short paths in a social network using only local information about their immediate contacts. We simulate such experiments on a network of actual email contacts within an organization as well as on a student social networking website. On the email network we find that small world search strategies using a contact's position in physical space or in an organizational hierarchy relative to the target can effectively be used to locate most individuals. However, we find that in the online student network, where the data is incomplete and hierarchical structures are not well defined, local search strategies are less effective. We compare our findings to recent theoretical hypotheses about underlying social structure that would enable these simple search strategies to succeed and discuss the implications to social software design.
... anisotropic [16] lattices -still a far cry, however, from the geographical spread and network of connections typical of human society. Dodds, Muhamad and Watts conducted a large-scale online experiment that resembles Milgram's original study, highlighting the role of information beyond just network structure [17]. Liben-Nowell et. ...
... other). Indeed, subject reports in Milgram-like experiments strongly support this idea [17]. The average path to the target's city in our simulations is significantly shorter than the total path ( Fig. 6(b)). ...
... We have shown that more complex strategies, such as occasionally passing the message to acquaintances that are especially well-connected, can result in a significant reduction of the path length. We have also confirmed the notion that geography is the most important consideration in finding short paths [17,18], at least in the initial stages, until the message reaches the target's city. The remaining path to the target, within the city, could be shortened considerably using the additional explicit information (e.g, occupation) and implicit information (ethnicity, social status) known about the target. ...
The study of social networks --- where people are located, geographically, and how they might be connected to one another --- is a current hot topic of interest, because of its immediate relevance to important applications, from devising efficient immunization techniques for the arrest of epidemics, to the design of better transportation and city planning paradigms, to the understanding of how rumors and opinions spread and take shape over time. We develop a spatial social complex network (SSCN) model that captures not only essential connectivity features of real-life social networks, including a heavy-tailed degree distribution and high clustering, but also the spatial location of individuals, reproducing Zipf's law for the distribution of city populations as well as other observed hallmarks. We then simulate Milgram's Small-World experiment on our SSCN model, obtaining good qualitative agreement with the known results and shedding light on the role played by various network attributes and the strategies used by the players in the game. This demonstrates the potential of the SSCN model for the simulation and study of the many social processes mentioned above, where both connectivity and geography play a role in the dynamics.
... However, in the late the 1990's a change of paradigm took place [4,5]. Physicists became interested in large scale social networks, utilizing electronic databases from emails [6,7,8] to phone records [9], offering unprecedented opportunities to uncover and explore large-scale social networks [10]. In this scheme the order of N ≈ 10 6 individuals may be handled and, although the range of social interactions is narrower, in some cases their strengths may be objectively quantifiable. ...
... Our result provides an empirical verification of the weak ties conjecture. It can also be related to a study dealing with search in social networks, according to which successful searches are conducted primarily through intermediate to weak strength ties without requiring highly connected hubs to succeed [8]. The present results suggest that the success of weak ties for search might lie in their function as community connectors, enabling one to reach outside of one's own community and thus expanding the set of individuals who may be reached through the network. ...
... Modern technologies enable the study of social networks of unprecedented size. A number of such investigations have appeared recently ranging from exploring email communication networks [6,7,8,47] to identifying groups and strategies in an electronic marketplace [48,49,50]. In this paper we constructed a network from mobile phone call records and used both aggregated call durations and the cumulative number of calls as a measure of the strength of a social tie. ...
We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well as its topological assortativity and weighted assortativity, clustering and weighted clustering, together with correlations between these quantities. We give an account of motif intensity and coherence distributions and compare them to a randomized reference system. We also use the concept of link overlap to measure the number of common neighbors any two adjacent nodes have, which serves as a useful local measure for identifying the interconnectedness of communities. We report a positive correlation between the overlap and weight of a link, thus providing strong quantitative evidence for the weak ties hypothesis, a central concept in social network analysis. The percolation properties of the network are found to depend on the type and order of removed links, and they can help understand how the local structure of the network manifests itself at the global level. We hope that our results will contribute to modeling weighted large-scale social networks, and believe that the systematic approach followed here can be adopted to study other weighted networks.
... This research questions the structural approach and contends that SNA method regularly exceeds the threshold of critical group size (Dodds, Muhamad, and Watts 2003;Friedman 1980;Hutchinson 2021;Kraut 1998) as it goes well beyond the personal network as well as the whole network size (Lubbers, Verdery, and Molina 2018). Individuals look captive in their networks that otherwise decide their assimilation (homogeneity) as well as their social diversity (transnationalism). ...
... These theresholds affect the rythm of exchange of infuences among human beings, and thus within social organizations dependent on the numerical value of these theresholds (Friedman 1980). Usually, it is accepted that every person is indirectly associated with every other person through an average of approximately six intermediaries (Dodds, Muhamad, and Watts 2003;Friedman 1980). This is the primary group or personal community that certain SNA researchers allude to as well (Marsden 2011). ...
... Ultimately, it is worth noting that Christmas gifts, rather than cards, signify the people with whom we share social intimacy. Usually, it is accepted that every person is indirectly associated with every other person through an average of approximately six intermediaries (Dodds, Muhamad, and Watts 2003;Friedman 1980). This is the primary group or personal community that certain SNA researchers allude to as well (Marsden 2011). ...
Social simultaneity describes individuals active in multiple social contexts. Migrant networks serve as a case study where social network analysis has been recently applied to assess their assimilation and transnationality. Yet, networks are sometimes insubstantial as all nominated nodes and bridges are part of the network graph except they are not part of the social grouping. This research attempts to look beyond the metaphor of social networks as it reviews critical group size theory and complements social network analysis with mixed methods of network survey and ethnographic interpretation. The article questions the structural approach and argues that interactions among alters may not be accurately recorded by this method. A respondent-driven sampling method was used to select and survey 55 egocentric networks out of 248 Romanian migrant networks in Spain. Results endorse precautions of critical group size theory that do not fit prescriptions of social network analysis. With technology acting as a go-between for individuals’ interactions, society has grown accustomed to being increasingly networked as individuals rather than socially embedded in groups. Online social networks provide interactions but not social embeddedness as suggested by the structural approach. The article concludes that smooth social integration and neoteric cultural diversity highlight features of third-generation migration in Europe. Despite this, the number of Romanians in Spain decreased at the end of the COVID-19 pandemic.
Keywords: migration, embeddedness, transnationalism, social network, critical group size
... It might be thought that the massive increase in connectivity since the discovery that people could connect with complete strangers through about five intermediaries (Travers & Milgram 1969) would drastically shrink the small world of interpersonal communication. But research suggests that it still takes between about five and seven intermediaries for e-mail users to reach target persons by forwarding messages through acquaintances (Dodds, Muhamad & Watts 2003). ...
... Presciently, weak tie theory in its earliest formulation (Granovetter 1973), linked Milgram's (1967) work on small-worlds to weak ties, noting how distant individuals are more likely to be reached through acquaintances than friendsan insight replicated in more recent small-world research (e.g., Dodds et al. 2003). In small-world terminology, "long-range shortcuts" (Watts, 1999: 511) tend to be weak ties, connecting what would otherwise be distant parts of a network involving long path lengths. ...
... Formation or deletion of weak ties at the local level can therefore have significant consequences on structural integration or fragmentation at the global level. Local processes such as formation of weak ties, for instance, have been characterized as contributing to the formation of a small-world at the global level, where highly clustered groups are connected by short path-lengths (Dodds et al. 2003;Robins, Pattison & Woolcock 2005). Thus, a powerful contribution of weak tie theory is in explaining how local network changes shape global network connectivity, a point less emphasized in structural hole theory. ...
This Element synthesizes the current state of research on organizational social networks from its early foundations to contemporary debates. It highlights the characteristics that make the social network perspective distinctive in the organizational research landscape, including its emphasis on structure and outcomes. It covers the main theoretical developments and summarizes the research design questions that organizational researchers face when collecting and analyzing network data. Then, it discusses current debates ranging from agency and structure to network volatility and personality. Finally, the Element envisages future research directions on the role of brokerage for individuals and communities, network cognition, and the importance of past ties. Overall, the Element provides an innovative angle for understanding organizational social networks, engaging in empirical network research, and nurturing further theoretical development on the role of social interactions and connectedness in modern organizations.
... To construct predictive J matrices we consider each system's specific interaction mechanisms. For example, in epidemic dynamics, individuals interact through infection and recovery, 9,26,27 in biological networks, proteins, genes and metabolites are linked through biochemical processes 11,12,29,31 and in population dynamics, species undergo competitive or symbiotic exchanges. 13,15,33,35 Quite generally, these dynamic mechanisms can be represented by ...
... In a similar fashion, the global interaction rate g increases/decreases the strength of all interactions, while the specific i, j interaction strength is governed by the potentially diverse weight matrix G ij . Together, (2.1) provides a generic template, allowing, by appropriately selecting M q (x), to cover a range of frequently used models in social, 9,26 biological [11][12][13]29,31 and technological 36 systems ( Fig. 2; see Methods Section 4 and Supplementary Section 1 for an expanded discussion of Eq. (2.1)). ...
... recovering the asymptotic scaling relationship of Eq. (4). In (26) we eliminated all terms that do not contribute to the polynomial dependence on d i , thus focusing solely on the obtained scaling relationship. These terms may, however, depend on other parameters of (2.1). ...
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, real-world networks often appear random and highly irregular, raising the question of what are the naturally emerging organizing principles of complex system stability. The answer is encoded within the system’s stability matrix—the Jacobian—but is hard to retrieve, due to the scale and diversity of the relevant systems, their broad parameter space and their nonlinear interaction dynamics. Here we introduce the dynamic Jacobian ensemble, which allows us to systematically investigate the fixed-point dynamics of a range of relevant network-based models. Within this ensemble, we find that complex systems exhibit discrete stability classes. These range from asymptotically unstable (where stability is unattainable) to sensitive (where stability abides within a bounded range of system parameters). Alongside these two classes, we uncover a third asymptotically stable class in which a sufficiently large and heterogeneous network acquires a guaranteed stability, independent of its microscopic parameters and robust against external perturbation. Hence, in this ensemble, two of the most ubiquitous characteristics of real-world networks—scale and heterogeneity—emerge as natural organizing principles to ensure fixed-point stability in the face of changing environmental conditions.
... After early studies on the structure of social networks by Michael Gurevich [2] and Manfred Kochen [3], Stanley Milgram performed his 1967 famous set of experiments on social distancing [4,5] where, with a limited sample of a thousand individuals, it was shown that people in the United States are indeed connected by a small number of acquaintances. Later on, Duncan Watts recreated Milgram's experiments with Internet email users [6] by tracking 24,163 chains aimed at 18 targets from 13 countries and confirmed that the average number of steps in the chains was around six. Furthermore, many experiments conducted at a planetary scale on various social networks verified the ubiquitous character of this feature: i) a 2007 study by Jure Leskovec and Eric Horvitz (with a data set of 30 billion conversations among 240 million Microsoft Messenger users) revealed the average path length to be 6 [7,8], ii) the average degree of separation between two randomly selected Twitter users was found to be 3.435 [9], and iii) the Facebook's network in 2011 (721 million users with 69 billion friendship links) displayed an average distance between nodes of 4.74 [10]. ...
... In this Article we rigourously show that, when a simple compensation rule between the cost incurred by nodes in maintaining connections and the benefit accrued by the chosen links is governing the evolution of a network, the asymptotic equilibrium state (a Nash equilibrium where no further actions would produce more benefit than cost [11]), features a diameter which does not depend on the system's size, and is equal to 6. In other words, we theorematically prove that any network where nodes strive to increase their centrality by forming connections if and only if their cost is smaller than the payoff tends to evolve into an ultra-small world state endowed with the 'six degree of separation' property, irrespective of its initial structure. ...
... (2)−f(6) + 2 ⇔ N < 2c f (2)−f (6) + 2 · (k 2 + 1) =⇒ N < 2 f (2)−f(6) (c + f (2) − f (6)) (k 2 + 1) ...
A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultra-small world organization, whereby the graph's diameter is independent of the network size over several orders of magnitude, is still unknown. Here we show that the 'six degrees of separation' are the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.
... In a review of Small World studies in small geographic contexts, Schnettler found the arithmetic means of chain lengths to be even smaller, ranging from just 1.8-5.7 intermediary contacts (see Schnettler, 2009aSchnettler, , 2009b. Dodds et al. (2003) global-level study of chain lengths estimated that globally, any two individuals are connected by a median of five to seven intermediary contacts. Newman et al. (2006) proposed that five intermediaries are needed to connect two distant persons via a chain of acquaintances. ...
... We see the efficacy of a research recruitment method employing criterion-based targeted searches via chains of referrals within a defined social network which also offers more information about the number of intermediary contact links between sets of individuals. (Adamic and Adar, 2005;Dodds et al., 2003;Killworth et al., 2006;Killworth and Bernard, 1978;Korte and Milgram, 1970;Travers and Milgram, 1969). ...
One primary concern in researching journalistic practice and media production is the difficulty of gaining research access to media organizations and their media professionals. This paper theorizes Small World Sampling method for identifying and recruiting participants for qualitative research. Based on an ethnographic interview study involving 32 journalists at six different international news organizations, our Small World Sampling method created a direct research path into journalists’ professional occupational networks without having to negotiate indirect access through their non-journalist organizational gatekeepers (e.g. PR executives, HR department, managers). Small World Sampling allows the participant selection process to be guided by media practitioners’ expert and in-group knowledge of their professional network of media colleagues and acquaintances. More methodologically important, our Small World Sampling protocol offers a novel technique for demonstrating the qualitative reliability of the sampling process and for establishing the qualitative validity of the sample under study. Additionally, the paper introduces the concept of ‘contextual case studies’ offering additional nuance and insights enriching the conclusions drawn from the project’s main case studies. Beyond media and journalism research, we propose that Small World Sampling may also prove useful for other fields to facilitate research access into closed organizations, elite networks, and hidden communities.
... One reason for this is, of course, that humans give up rather than visit thousands of nodes. To account for this, we compute an ideal curve for the hypothetical case that humans are forced to finish every mission, based on measured drop-out rates (Dodds, Muhamad, and Watts 2003). We find that even then, the human curve (dashed black) starts to overtake the others around T = 9. ...
... Decentralized search is similar to the setup we study, in that a target node is to be reached via local navigation only. The analysis of such processes was kick-started by Milgram's (1967) seminal 'small world' experiment, later repeated on a larger scale by Dodds, Muhamad, and Watts (2003). Theoretical analyses of the properties a network must have to warrant efficient decentralized search (Kleinberg 2000;Liben-Nowell et al. 2005) showed that just the right amount of homophily is both necessary and sufficient, which gives rise to similarity-based navigation. ...
People regularly face tasks that can be understood as navigation in information networks, where the goal is to find a path between two given nodes. In many such situations, the navigator only gets local access to the node currently under inspection and its immediate neighbors. This lack of global information about the network notwithstanding, humans tend to be good at finding short paths, despite the fact that real-world networks are typically very large. One potential reason for this could be that humans possess vast amounts of background knowledge about the world, which they leverage to make good guesses about possible solutions. In this paper we ask the question: Are human-like high-level reasoning skills really necessary for finding short paths? To answer this question, we design a number of navigation agents without such skills, which use only simple numerical features. We evaluate the agents on the task of navigating Wikipedia, a domain for which we also possess large-scale human navigation data. We observe that the agents find shorter paths than humans on average and therefore conclude that, perhaps surprisingly, no sophisticated background knowledge or high-level reasoning is required for navigating the complex Wikipedia network.
... The diameter is usually smaller than the number of nodes. Even the largest real-world social networks are estimated to have diameters of less than 6, which can make the world feel small when it comes to connecting people [34]. There are also relationships to be observed between social network statistics. ...
This study explores communication structures in construction design offices using social network analysis (SNA) to compare directed and undirected networks. The objective is to understand how these network types influence hierarchy, information flow, and collaboration within small design teams. Data were collected from nine construction design offices, constructing both directed and undirected networks based on survey responses. Various graph theory metrics, including clustering coefficient, network diameter, centrality, and connectivity, were analyzed to assess communication efficiency. The results show that directed networks emphasize hierarchical structures with limited reciprocal exchanges, while undirected networks confirm mutual interactions, fostering collaboration. Despite variations in size, most networks exhibit small-world properties, indicating that key individuals act as bridges, ensuring effective communication. These findings highlight that network structure, rather than size, plays a crucial role in team coordination. This study contributes to Architecture, Engineering, and Construction (AEC) research by providing insights into optimizing team dynamics, balancing hierarchical control with flexible collaboration, and improving project management strategies. Doi: 10.28991/CEJ-2025-011-03-02 Full Text: PDF
... This study provides evidence information to improve self-management and awareness of post-stroke symptoms, diffuse in an OHC, and for the key role played by highly active users [35] in distributing its linked benefits to an entire community of patients. ...
Background:
Online health communities (OHCs) enable patients to create social ties with people with similar health conditions outside their existing social networks. Harnessing mechanisms of information diffusion in OHCs has attracted attention for its ability to improve illness self-management without the use of health care resources.
Objective:
We aimed to analyze the novelty of a metaphor used for the first time in an OHC, assess how it can facilitate self-management of post-stroke symptoms, describe its appearance over time, and classify its diffusion mechanisms.
Methods:
We conducted a passive analysis of posts written by UK stroke survivors and their family members in an online stroke community between 2004 and 2011. Posts including the term “legacy of stroke” were identified. Information diffusion was classified according to self-promotion or viral spread mechanisms and diffusion depth (the number of users the information spreads out to). Linguistic analysis was performed through the British National Corpus and the Google search engine.
Results:
Post-stroke symptoms were referred to as “legacy of stroke.” This metaphor was novel and appeared for the first time in the OHC in the second out of a total of 3459 threads. The metaphor was written by user A, who attributed it to a stroke consultant explaining post-stroke fatigue. This user was a “superuser” (ie, a user with high posting activity) and self-promoted the metaphor throughout the years in response to posts written by other users, in 51 separate threads. In total, 7 users subsequently used the metaphor, contributing to its viral diffusion, of which 3 were superusers themselves. Superusers achieved the higher diffusion depths (maximum of 3). Of the 7 users, 3 had been part of threads where user A mentioned the metaphor, while 2 users had been part of discussion threads in unrelated conversations. In total, 2 users had not been part of threads with any of the other users, suggesting that the metaphor was acquired through prior lurking activity.
Conclusions:
Metaphors that are considered helpful by patients with stroke to come to terms with their symptoms can diffuse in OHCs through both self-promotion and social (or viral) spreading, with the main driver of diffusion being the superuser trait. Lurking activity (the most common behavior in OHCs) contributed to the diffusion of information. As an increasing number of patients with long-term conditions join OHCs to find others with similar health-related concerns, improving clinicians’ and researchers’ awareness of the diffusion of metaphors that facilitate self-management in health social media may be beneficial beyond the individual patient.
... White et al. (1976) demonstrated in 1976 that it is possible to efficiently extract an image of social structure underlying multiple relations defined for the same set of actors. Watts et al. (2002), based on the results of Travers and Milgram (1969) as well as their own recent electronic experiment (Dodds et al., 2003), proposed that people use multiple relations in order to solve the small world problem, i.e. to deliver a message to an unknown target using only connections from within their egocentric network. In both studies, however, the number of actors is much greater than the number of relations in which actors participate. ...
We perform sensitivity analyses to assess the impact of missing data on the structural properties of social networks. The social network is conceived of as being generated by a bipartite graph, in which actors are linked together via multiple interaction contexts or affiliations. We discuss three principal missing data mechanisms: network boundary specification (non-inclusion of actors or affiliations), survey non-response, and censoring by vertex degree (fixed choice design), examining their impact on the scientific collaboration network from the Los Alamos E-print Archive as well as random bipartite graphs. The results show that network boundary specification and fixed choice designs can dramatically alter estimates of network-level statistics. The observed clustering and assortativity coefficients are overestimated via omission of interaction contexts (affiliations) or fixed choice of affiliations, and underestimated via actor non-response, which results in inflated measurement error. We also find that social networks with multiple interaction contexts have certain surprising properties due to the presence of overlapping cliques. In particular, assortativity by degree does not necessarily improve network robustness to random omission of nodes as predicted by current theory.
... Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing (alternatively navigation or search) works or should work in real networks [1][2][3][4][5][6][7]. However, these assumptions are rarely checked against real data [8,9]. Here we directly analyze the structure of operational paths using real measurements. ...
Various hypotheses exist about the paths used for communication between the nodes of complex networks. Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing (alternatively navigation or search) works or should work in real networks. However, these assumptions are rarely checked against real data. Here we directly analyze the structure of operational paths using real measurements. For this purpose we use existing and newly created datasets having both the topology of the network and a sufficient number of empirically-determined paths over it. Such datasets are processed for air transportation networks, the human brain, the Internet and the fit-fat-cat word ladder game. Our results suggest that from the great number of possible paths, nature seems to pick according to some simple rules, which we will refer to as routing policies. First we confirm, that the preference of short paths is an inevitable policy element, however the observed stretch of the paths suggests that there are other policies at work simultaneously. We identify two additional policies common in our networks: the "conform hierarchy", meaning that the paths should obey the structural hierarchy of the network, and the "prefer downstream" policy which promotes avoiding the network core if possible. Building upon these simple policies, we propose a synthetic routing policy which can recover the basic statistical properties of the operational paths in networks. Our results can be helpful in estimating the reaction of complex systems for stress coming from the outside more accurately than the shortest path assumption permits.
... In social networks, such small distances go under the name of the 'six-degrees-ofseparation' paradigm and have attracted attention due to the interesting experiments by Milgram [41,59]. See also Pool and Kochen [55] as well as [17], where a related experiment is described on the basis on email messages. After this start in social sciences, the small-world nature of many other networks was first described by Strogatz and Watts [62]. ...
In this paper we study typical distances in the configuration model, when the degrees have asymptotically infinite variance. We assume that the empirical degree distribution follows a power law with exponent , up to value for some and . This assumption is satisfied for power law i.i.d. degrees, and also includes truncated power-law distributions where the (possibly exponential) truncation happens at . We show that the graph distance between two uniformly chosen vertices centers around , with tight fluctuations. Thus, the graph is an \emph{ultrasmall world} whenever . We determine the distribution of the fluctuations around this value, in particular we prove that these are non-converging tight random variables that show -periodicity. We describe the topology and number of shortest paths: We show that the number of shortest paths is of order , where is a random variable that oscillates with n. The two end-segments of any shortest path have length +tight, and the total degree is increasing towards the middle of the path on these segments. The connecting middle segment has length +tight, and it contains only vertices with degree at least of order , thus all the degrees on this segment are comparable to the maximal degree. Our theorems also apply when instead of truncating the degrees, we start with a configuration model and we remove every vertex with degree at least , and the edges attached to these vertices. This sheds light on the attack vulnerability of the configuration model with infinite variance degrees.
... However, similar to the widespread use of the expression 'six degrees of separation,' this turn of phrase is meant to be evocative, not definitive. For instance, even the widely discussed 'six degrees of separation' is not precisely six, neither in Milgram's classic paper [59] nor Watts and colleagues' clever, well known email experiment [60]. ...
Here, we review the research we have done on social contagion. We describe the methods we have employed (and the assumptions they have entailed) in order to examine several datasets with complementary strengths and weaknesses, including the Framingham Heart Study, the National Longitudinal Study of Adolescent Health, and other observational and experimental datasets that we and others have collected. We describe the regularities that led us to propose that human social networks may exhibit a "three degrees of influence" property, and we review statistical approaches we have used to characterize inter-personal influence with respect to phenomena as diverse as obesity, smoking, cooperation, and happiness. We do not claim that this work is the final word, but we do believe that it provides some novel, informative, and stimulating evidence regarding social contagion in longitudinally followed networks. Along with other scholars, we are working to develop new methods for identifying causal effects using social network data, and we believe that this area is ripe for statistical development as current methods have known and often unavoidable limitations.
... The findings of this study revealed a fascinating distribution in the choice of initial contacts: friends were the most common starting point (67%), followed by family members (10%), and colleagues (9%). On average, the chain of communication required between 5 and 7 intermediaries to connect with unknown individuals, reinforcing the validity of the small world hypothesis in an Internet's setting (Muhamad et al., 2003). Importantly, the research underscored the predominance of social and professional connections over familial or casual ties in navigating these networks. ...
This study explored the transformative effects of e-recruitment on recruiter-candidate engagement, with a focus on the Moroccan job market's challenges in feedback and interaction. Despite the widespread adoption of digital platforms enhancing job vacancy accessibility, this study revealed a persistent feedback gap, particularly in Morocco. A comparative analysis involving 200 job advertisements from Moroccan and French companies, supplemented by insights from HR professionals, highlights the differential response rates and feedback mechanisms. Our findings indicate a significant underutilisation of advanced technologies, such as artificial intelligence (AI), that could improve recruitment efficiency and candidate experience. Through a multidimensional approach, this paper offers strategic recommendations for leveraging digitalisation to revitalise HR practices, emphasising the need for Moroccan companies to adopt AI and enhance digital infrastructure for a more dynamic and inclusive recruitment process.
... As previously discussed, our inspiration for studying this problem is Milgram's "small world" experiment [12]. The findings, later validated on a larger scale [27], support this hypothesis in social networks, which are characterized by short mean path lengths. Subsequent research [28] highlighted the discovery of effective routing strategies, emphasising the concept of homophily [15], which states that individuals seek connections to others that are similar to themselves. ...
Graph path search is a classic computer science problem that has been recently approached with Reinforcement Learning (RL) due to its potential to outperform prior methods. Existing RL techniques typically assume a global view of the network, which is not suitable for large-scale, dynamic, and privacy-sensitive settings. An area of particular interest is search in social networks due to its numerous applications. Inspired by seminal work in experimental sociology, which showed that decentralized yet efficient search is possible in social networks, we frame the problem as a collaborative task between multiple agents equipped with a limited local view of the network. We propose a multi-agent approach for graph path search that successfully leverages both homophily and structural heterogeneity. Our experiments, carried out over synthetic and real-world social networks, demonstrate that our model significantly outperforms learned and heuristic baselines. Furthermore, our results show that meaningful embeddings for graph navigation can be constructed using reward-driven learning.
... This setting is based on the theory of six degrees of separation, which posits that in social networks, any two individuals are, on average, connected by only five intermediaries (or six steps) to establish contact [38]. This theory has gained further support and development within the context of social networks and big data analysis [39,40]. Additionally, the small-world network model effectively simulates real-world social networks' structure, particularly in describing population clustering and social interactions [41,42]; After January 23rd, Wuhan was "closed, " all public transportation was halted, and all long-distance connections were cut off. ...
Background
The rapid global spread of COVID-19 has seriously impacted people’s daily lives and the social economy while also posing a threat to their lives. The analysis of infectious disease transmission is of significant importance for the rational allocation of epidemic prevention and control resources, the management of public health emergencies, and the improvement of future public health systems.
Methods
We propose a spatiotemporal COVID-19 transmission model with a neighborhood as an agent unit and an urban spatial network with long and short edge connections. The spreading model includes a network of defined agent attributes, transformation rules, and social relations and a small world network representing agents’ social relations. Parameters for each stage are fitted by the Runge-Kutta method combined with the SEIR model. Using the NetLogo development platform, accurate dynamic simulations of the spatial and temporal evolution of the early epidemic were achieved.
Results
Experimental results demonstrate that the fitted curves from the four stages agree with actual data, with only a 12.27% difference between the average number of infected agents and the actual number of infected agents after simulating 1 hundred times. Additionally, the model simulates and compares different “city closure” scenarios. The results showed that implementing a ‘lockdown’ 10 days earlier would lead to the peak number of infections occurring 7 days earlier than in the normal scenario, with a reduction of 40.35% in the total number of infections.
Discussion
Our methodology emphasizes the crucial role of timely epidemic interventions in curbing the spread of infectious diseases, notably in the predictive assessment and evaluation of lockdown strategies. Furthermore, this approach adeptly forecasts the influence of varying intervention timings on peak infection rates and total case numbers, accurately reflecting real-world virus transmission patterns. This highlights the importance of proactive measures in diminishing epidemic impacts. It furnishes a robust framework, empowering policymakers to refine epidemic response strategies based on a synthesis of predictive modeling and empirical data.
... It has been observed that individuals within social networks are separated by no more than six degrees of separation from any other individual on the planet, commonly known as the small world effect [26]. This phenomenon has been validated in several social networks, including Stanley Milgram's pioneering letter-passing experiment [27] and studies of massive online communication networks [28,29]. We show that on a European scale firm-level production networks can be classified as small worlds. ...
Globalization has had undesirable effects on the labor standards embedded in the products we consume. This paper proposes an ex-ante evaluation of supply chain due diligence regulations, such as the EU Corporate Sustainable Due Diligence Directive (CSDDD). We construct a full-scale network model derived from structural business statistics of 30 million EU firms to quantify the likelihood of links to firms potentially involved in human rights abuses in the European supply chain. The 900 million supply links of these firms are modeled in a way that is consistent with multiregional input-output data, EU import data, and stylized facts of firm-level production networks. We find that this network exhibits a small world effect with three degrees of separation, meaning that most firms are no more than three steps away from each other in the network. Consequently we find that about 8.5% of EU companies are at risk of having child or forced labor in the first tier of their supply chains, about 82.4% are likely to have such offenders at the second tier and more than 99.1% have such offenders at the third tier. We also profile companies by country, sector, and size for the likelihood of having human rights violations or child and forced labor violations at a given tier in their supply chain, revealing considerable heterogeneity across EU companies. Our results show that supply chain due diligence regulations that focus on monitoring individual buyer-supplier links, as currently proposed in the CSDDD, are likely to be ineffective due to a high degree of redundancy and the fact that individual company value chains cannot be properly isolated from the global supply network. Rather, to maximize cost-effectiveness without compromising due diligence coverage, we suggest that regulations should focus on monitoring individual suppliers.
... For example, network studies in the small-data era heavily rely on exquisite experimental design, such as the small-world experiment conducted by sociologist Stanley Milgram to examine the average path length and social networks in the United States (Travers & Milgram, 1967). Compared to the original research procedures, which was tracking and analyzing the postcards mailing between Nebraska and Kansa, the big data-driven replication of it involved over 24,000 emails chains and extended the geographic scope to the entire earth (Dodds et al., 2003). Zoomed into more recent studies, the network attributes of human mobility patterns attracted great research interest and contribute greatly to accelerating interdisciplinary dialogues (Alessandretti et al., 2020;Sun et al. 2013;). ...
Considered a total social phenomenon, mobility is at the center of intricate social dynamics in cities and serves as a reading lens to understand the whole society. With the advent of big data, the potential for using mobility as a key social analyzer was unleashed in the past decade. The purpose of this research is to systematically review the evolution of big data's role in revealing social dimensions of urban mobility and discuss how they have contributed to various research domains from early 2010s to now. Six major research topics are detected from the selected online academic corpuses by conducting keywords-driven topic modeling techniques, reflecting diverse research interests in networked mobilities, human dynamics in spaces, event modeling, spatial underpinnings, travel behaviors and mobility patterns, and sociodemographic heterogeneity. The six topics reveal a comprehensive, research-interests, evolution pattern, and present current trends on using big data to uncover social dimensions of human mobility activities. Given these observations, we contend that big data has two contributions to revealing social dimensions of urban mobility: as an efficiency advancement and as an equity lens. Furthermore, the possible limitations and potential opportunities of big data applications in the existing scholarship are discussed. The review is intended to serve as a timely retrospective of societal-focused mobility studies, as well as a starting point for various stakeholders to collectively contribute to a desirable future in terms of mobility.
... More formally, small-world networks have a low average path length, which is the main characteristic of the small-world networks. There have been experiments (Dodds et al., 2003) demonstrating that the world indeed possesses this property and outside of the mathematical community, it is widely known as six degrees of separation (Wikipedia contributors, 2019). Small-World networks can be seen as scale-free networks with the additional property of having distinct connected clusters. ...
Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in the domain of image processing, where Convolutional Neural Networks are used. Although excelling at image classification, Convolutional Neural Networks are quite naive in that no inductive bias is set on the embedding space for images. Similar flaws are also exhibited by another type of Convolutional Networks - Graph Convolutional Neural Networks. However, using non-Euclidean space for embedding data might result in more robust and explainable models. One example of such a non-Euclidean space is hyperbolic space. Hyperbolic spaces are particularly useful due to their ability to fit more data in a low-dimensional space and tree-likeliness properties. These attractive properties have been previously used in multiple papers which indicated that they are beneficial for building hierarchical embeddings using shallow models and, recently, using MLPs and RNNs. However, no papers have yet suggested a general approach to using Hyperbolic Convolutional Neural Networks for structured data processing, although these are the most common examples of data used. Therefore, the goal of this work is to devise a general recipe for building Hyperbolic Convolutional Neural Networks. We hypothesize that ability of hyperbolic space to capture hierarchy in the data would lead to better performance. This ability should be particularly useful in cases where data has a tree-like structure. Since this is the case for many existing datasets \citep{wordnet, imagenet, fb15k}, we argue that such a model would be advantageous both in terms of applications and future research prospects.
... In the other, researchers focus on the effectiveness or efficiency of an algorithm that measures social influence (Lamertz, 2002;Kiss and Bichler, 2008;Eckhardt et al., 2009). In examining the effects of social influence, previous studies commonly analyze the scope (i.e., how many social ties they have) and/or the strength of their social connections (i.e., how frequently they interact with others) (Dodds et al., 2003;Krackhardt et al., 2003;Zhao, 2006;Steffes and Burgee, 2009). However, little is known about the effect of social influence generated by social position on economic behaviors such as product choice (Henrich, 2000;Manski, 2000). ...
... Including even more sporadic potential work connections, that is, all of the larger workplaces, further decreases average distances to 4.64, that approaches the value suggested for Facebook by Backstrom et al. 5 . It also provides empirical confirmation of the findings of Dodds et al. 29 , who suggest that shortest paths in large-scale networks are likely to be mediated by professional or school connections. ...
Large-scale human social network structure is typically inferred from digital trace samples of online social media platforms or mobile communication data. Instead, here we investigate the social network structure of a complete population, where people are connected by high-quality links sourced from administrative registers of family, household, work, school, and next-door neighbors. We examine this multilayer social opportunity structure through three common concepts in network analysis: degree, closure, and distance. Findings present how particular network layers contribute to presumably universal scale-free and small-world properties of networks. Furthermore, we suggest a novel measure of excess closure and apply this in a life-course perspective to show how the social opportunity structure of individuals varies along age, socio-economic status, and education level.
... After early studies on the structure of social networks by Gurevitch [2] and de Sola Pool and Kochen [3], Milgram performed his 1967 famous set of experiments on social distancing [4] (see also Ref. [5]) where, with a limited sample of 1000 individuals, it was shown that people in the U.S. are indeed connected by a small number of acquaintances. Later on, Dodds et al. recreated Milgram's experiments with Internet email users [6] by tracking 24 163 chains aimed at 18 targets from 13 countries and confirmed that the average number of steps in the chains was around six. Furthermore, many experiments conducted at a planetary scale on various social networks verified the ubiquitous character of this feature: (i) a 2007 study by Leskovec and Horvitz (with a dataset of 30 billion conversations among 240 million Microsoft Messenger users) revealed the average path length to be six [7] (see also Ref. [8]), (ii) the average degree of separation between two randomly selected Twitter users was found to be 3.435 [9], and (iii) Facebook's network in 2011 (721 million users with 69 billion friendship links) displayed an average distance between nodes of 4.74 [10]. ...
A wealth of evidence shows that real-world networks are endowed with the small-world property, i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultrasmall-world organization, whereby the graph’s diameter is independent of the network size over several orders of magnitude, is still unknown. We show that the “six degrees of separation” is the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. We show, moreover, that the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.
... Many facilities and systems in real life can be abstracted into networks, such as transportation networks, biological networks, financial networks, electric networks, and social networks. [1][2][3][4][5][6][7][8][9] These networks have brought convenience to human production and life, while the propagation phenomena occurring on the networks have also brought negative effects, and complex networks science provides theories and analytical methods for studying complex systems in the real world. ...
In this paper, an edge-coupled interdependent networks with directed dependency links (EINDDL) model is proposed, and the theoretical analysis framework of this model based on the self-consistent probabilities method is developed. The phase transition behaviors and parameter thresholds of this model under random attacks are analyzed theoretically on both Random Regular ( RR ) networks and Erdös-Rényi ( ER ) networks, and computer simulation are performed to verify the results. In this EINDDL model, a fraction β of connectivity links within network B depends on network A and a fraction (1 - β ) of connectivity links within network A depends on network B . It is found that randomly removing a fraction 1- p of connectivity links in network A at the initial state, network A exhibits different types of phase transitions (first-order, second-order and hybrid). Network B is rarely affected by cascading failure when β is small, and network B will gradually converge from the first-order to the second-order phase transition as β increases. The critical values of β for the phase changes process of network A and network B , and the critical values of p and β for network B at the critical point of collapse are given. Furthermore, a cascading prevention strategy is proposed. The findings are of great significance for understanding the robustness of EINDDL.
... With a large advice-giving network, it will be more likely for colleagues in the network to possess duplicative skills or redundant resources. Reciprocation from coworkers with non-unique skills or resources likely generates a lesser value for the information provider (Dodds, Muhamad, & Watts, 2003;Rodan & Galunic, 2004). As advice-giving ties grow to a large size, individuals are likely to lose track of the coworkers in their advice-giving network they can tap on for support and help when called for. ...
Existing research examining the curvilinear relationship between network centrality and performance tends to focus on the information recipients’ perspective. Focusing on the information providers’ perspective, our study draws upon social exchange theory to demonstrate that the advice-giving centrality-performance relationship for information providers has an inverse U-shape due to decreasing benefits and increasing costs of maintaining more advice-giving ties. We further show that increasing advice-giving centrality increases the likelihood that individuals would become a hindrance to coworkers, as they become bottlenecks impeding efficient workflow. However, our study demonstrates that political skill enables them to overcome the interpersonal challenges associated with high advice-giving centrality. Specifically, individuals with high political skills can better convert advice-giving ties to resources that could assist their cooperation with coworkers, reducing the hindrance they impose. Overall, we provide insights into the trade-off between the benefits and costs of advice-giving ties from a social exchange perspective and examine political skill as an important mitigator of the downsides of large advice-giving networks – a key area that has been hitherto largely unexplored.
... The complex network, as a branch of the system science, has become a hot research field that explores the relationships among different objects. From then on, complex networks have already been applied in various fields and get many interesting results (Dodds et al. 2003;Newman 2001;Strogatz 2001;Barabási et al. 2011). ...
Consider chemical elements as a system, we create an undirected chemical network with 99 elements and 1916 edges from Chemspider, a website that provide search engines to collect compounds. Using this network and the network that we used in our previous work with 97 elements and 2198 edges, we found that RootedPageRank, a link prediction tool in complex network, can be used to predict potential binary compounds, because the changing trend of PageRank probability of each element in these networks all follow the periodic law, despite of the difference of scale of these networks. The accuracy test indicates that at least 7 among top 10 predicted compoundss in one network can be verified using the compoundss in the other network or in other chemical database, proving that this method can be used to provide guidance in finding potential binary compounds, suggesting that we can study chemical properties from the view of complex network.
... It also provides empirical confirmation of the findings of (Dodds et al. 2003), who suggest that shortest paths in large-scale networks are likely to be mediated by professional or school connections. ...
Large-scale human social network structure is typically inferred from digital trace samples of online social media platforms or mobile communication data. Instead, here we investigate the social network structure of a complete population, where people are connected by high-quality links sourced from administrative registers of family, household, work, school, and next-door neighbors. We examine this multilayer social opportunity structure through three common concepts in network analysis: degree, closure, and distance. Findings present how particular network layers contribute to presumably universal scale-free and small-world properties of networks. Furthermore, we suggest a novel measure of excess closure and apply this in a life-course perspective to show how the social opportunity structure of individuals varies along age, socio-economic status, and education level. Our work provides new entry points to understand individual socio-economic failure and success as well as persistent societal problems of inequality and segregation.
... Network science have stood out as a representative model of complex systems due to their multidisciplinary character and ability to represent elements of a system and their interactions. Once the elements of the systems and their connectivity are established, networks can be used to model many real world applications, such as: Natural Phenomena [1,2,3], Biology [4,5,6], Social [7,8,9], Physical [10,11], etc. A classical example is the connectivity between routers and computers by cables and optical fibers, forming the well known Internet [12]. ...
Network modeling has proven to be an efficient tool for many interdisciplinary areas, including social, biological, transport, and many other real world complex systems. In addition, cellular automata (CA) are a formalism that has been studied in the last decades as a model for exploring patterns in the dynamic spatio-temporal behavior of these systems based on local rules. Some studies explore the use of cellular automata to analyze the dynamic behavior of networks, denominating them as network automata (NA). Recently, NA proved to be efficient for network classification, since it uses a time-evolution pattern (TEP) for the feature extraction. However, the TEPs explored by previous studies are composed of binary values, which does not represent detailed information on the network analyzed. Therefore, in this paper, we propose alternate sources of information to use as descriptor for the classification task, which we denominate as density time-evolution pattern (D-TEP) and state density time-evolution pattern (SD-TEP). We explore the density of alive neighbors of each node, which is a continuous value, and compute feature vectors based on histograms of the TEPs. Our results show a significant improvement compared to previous studies at five synthetic network databases and also seven real world databases. Our proposed method demonstrates not only a good approach for pattern recognition in networks, but also shows great potential for other kinds of data, such as images.
We draw attention to a clear dichotomy between small-world networks exhibiting exponential neighborhood growth, and fractal-like networks where neighborhoods grow according to a power law. This distinction is observed in a number of real-world networks, and is related to the degree correlations and geographical constraints. We conclude by pointing out that the status of human social networks in this dichotomy is far from clear.
Third parties who refer clients to expert service providers help clients navigate market uncertainty by curating well-tailored matches between clients and experts and by facilitating post-match trust. We argue that these two functions often entail trade-offs because they require referrers to activate network relationships with different experts. While strong ties between referrers and experts promote trust between clients and experts, the presence of such ties reduces the likelihood that intermediaries refer clients to socially distal experts who may be better suited to serve clients’ needs. We examine this central and unexplored tension by using full population medical claims data for the state of Massachusetts. We find that when primary care physicians (PCPs) refer patients to specialists with whom the PCPs have strong ties, patients demonstrate more confidence in the specialists’ recommendations. However, a strong tie between the PCP and specialist also reduces the expertise match between a patient’s health condition and a specialist’s clinical experience. These findings suggest that the two central means by which referrers add value may be at odds with one another because they are maximized by the activation of different network ties.
This research aims to investigate whether the diffusion of academic articles’ citations follows a random order. A social network analysis (SNA) is employed whereas articles’ citation networks were constructed based on multiple generations of citations. For example, the “first-generation citations” represent articles citing the original publication, whereas the second generation represents those citing the first-generation’s citations. Results revealed a heterogeneous hub-and-spoke network with relatively low density. In this network only a few influential articles within small communities appear to control the information diffusion through the network, lending strong support to the “Matthew Effect”, which is a variation of the “rich get richer” model. Such articles seem to form bridges between key clusters in the network through information brokerage in the network. The “small world preferential attachment” network linking the cited articles was also confirmed through statistical robustness checks.
Vertex cover (VC) problem is an important combinatorial optimization problem that has a wide range of applications. In this article, we investigate the existing works on solving the VC problem from game theoretic perspective; these works treated each vertex of a network as a completely rational player. In contrast, we consider the impact of player's subjective behavior, that is, each player is not necessarily completely rational. First, we establish a game model under the expected utility theory (EUT) and the framing effect (FE) of the prospect theory. Second, we analyze the relationship between VC and game model under the EUT and the FE. Third, we propose a relaxed greedy behavioral algorithm, and prove that our proposed algorithm can guarantee that the strategies of all vertices converge to a strict Nash equilibrium under the EUT and the FE. Finally, the simulation results not only evaluate the influence of FE on the overall cover level of networks but also demonstrate the effectiveness and superiority of our proposed algorithm compared with the existing bounded rationality algorithm on representative networks and standard benchmark.
In the 21st century, the issue of national security in relation to the actions of terrorist organizations remains relevant. With the development of digital and information and communication technologies, traditional hierarchical approaches in the fight against the enemy are not effective. New strategies and tools are needed that can identify decentralized structures, consisting of a number of loosely connected individuals, that allow modeling the structure and connections of a terrorist organization. Such a modern analytical tool is the analysis of social networks, as it allows you to establish social connections between people. The article provides an over-view of the history of social network analysis and its use in understanding the organization of terrorist networks and establishing existing and potential connections of terrorist organizations.
In the 1960 s, the world-renowned social psychologist Stanley Milgram conducted experiments that showed that not only do there exist “short chains” of acquaintances between any two arbitrary people, but that these arbitrary strangers are able to find these short chains. This phenomenon, known as the small-world phenomenon, is explained in part by any model that has a low diameter, such as the Barabási and Albert’s preferential attachment model, but these models do not display the same efficient routing that Milgram’s experiments showed. In the year 2000, Kleinberg proposed a model with an efficient greedy routing algorithm. In 2004, Martel and Nguyen showed that Kleinberg’s analysis was tight, while also showing that Kleinberg’s model had an expected diameter of only —a much smaller value than the greedy routing algorithm’s path lengths. In 2022, Goodrich and Ozel proposed the neighborhood preferential attachment model (NPA), combining elements from Barabási and Albert’s model with Kleinberg’s model, and experimentally showed that the resulting model outperformed Kleinberg’s greedy routing performance on U.S. road networks. While they displayed impressive empirical results, they did not provide any theoretical analysis of their model. In this paper, we first provide a theoretical analysis of a generalization of Kleinberg’s original model and show that it can achieve expected routing, a much better result than Kleinberg’s model. We then propose a new model, windowed NPA, that is similar to the neighborhood preferential attachment model but has provable theoretical guarantees w.h.p. We show that this model is able to achieve greedy routing for any .
As redes sociais na Internet experimentaram um grande e rápido crescimento nos últimos anos e congregam milhões de usuários no Brasil e no mundo. Tais redes permitem agregar grupos de pessoas, com relacionamentos ou interesses comuns, permitindo aos membros desse grupo comunicar-se e trocar informações. Algumas redes sociais possuem objetivos específicos como, por exemplo, a rede Linkedln, somente para profissionais. Contudo, todas elas compartilham de informações, seja na forma de mensagens curtas seja em fotos e vídeos, dentre outros. O compartilhamento de informações em arquivos é uma atividade também crescente na Internet e é realizada de diversas formas, como o envio de arquivos, através de e-mails para vários contatos ou a disponibilização em áreas compartilhadas. Contudo, ainda não estão disponíveis aplicativos que permitam o compartilhamento de arquivos no Facebook, considerada a principal rede social da atualidade. Dada a grande quantidade de usuários do Facebook, a familiaridade dos mesmos com o uso de aplicativos integrados ao Facebook e a crescente procura pelo compartilhamento de arquivos, constata-se que existe uma real demanda para aplicativos, que permitam aos usuários compartilhar arquivos com seus contatos nessa rede social. O presente trabalho busca investigar como os usuários utilizam o Facebook e quais são as suas práticas para compartilhamento de arquivos. Acredita-se que os resultados obtidos fundamentarão projetos futuros para o desenvolvimento de um software para compartilhamento de arquivos no Facebook. Devido ao caráter exploratório dessa investigação, optou-se por um survey para o levantamento de dados, aplicado pela web. A partir da análise dos dados, observou-se um uso frequente do compartilhamento de arquivos, mas sem interesse em serviços pagos. Quanto ao Facebook, observou-se o seu uso intenso, tanto na frequência de acesso e no tempo da conexão como no uso de aplicativos (jogos, quiz, etc). O conjunto dos resultados obtidos mostra um cenário favorável e uma necessidade imediata para o desenvolvimento de aplicativos que permitam o compartilhamento de arquivos no Facebook. Palavras-chave: Redes Sociais; Facebook; Internet; Tecnologia da Informação.
Considering that social network provides a channel for nodes to exchange information, resources, and interests, the fundamental task of social network search is to find the best path from the source node to the target node. The search strategy based on the shortest path principle ignores the strength and direction of the social relationship between nodes in the social network, and ignores the difference of influence between nodes, so that the search results cannot meet the needs of searchers. Considering the important role of the influence of nodes and the influence intensity between nodes in social network search, this paper proposes the path optimization principle of maximizing the comprehensive influence, and constructs a new search algorithm based on this strategy by applying the modified Dijkstra algorithm to solve the optimal path between nodes. Using the data of typical real social networks, it is verified that the path optimization algorithm based on the principle of maximizing comprehensive impact is better than the optimization algorithm based on the shortest path, and the search results are better interpretable to users. This paper had proposed a new influence maximization algorithm which has more advantages for solving social network search with high costs or benefits consideration by taking the influence intensity of nodes or between nodes into account.
Perbaikan atau kemajuan dalam pendidikan adalah salah satu latar belakang terjadinya inovasi pendidikan. Inovasi pendidikan merupakan suatu ide, produk, atau hasil karya baru yang bisa digunakan sebagai pembaharuan untuk mencapai tujuan pendidikan atau menyelesaikan permasalahan di dunia pendidikan. Perkembangan teknologi dan informasi yang semakin berkembang, tentunya juga berdampak pada berbagai aspek kehidupan yang salah satunya adalah bidang Pendidikan. Melalui inovasi pendidikan, diharapkan pendidikan mampu mengikuti perkembangan zaman. Sehingga kualitas pendidikan akan semakin baik dan terarah, serta dapat mencapai efisiensi dan efektivitas untuk mengembangkan potensi diri peserta didik dalam dunia Pendidikan. Pokok bahasan dalam buku “Inovasi Pendidikan” ini mencakup Konsep dan Karakteristik Inovasi Pendidikan, Lesson Study Sebagai Inovasi Pembelajaran, Inovasi dan Kategori Adopter, Opinion Leader dan Jaringan Difusi, PTK Sebagai Inovasi Pembelajaran, Konsekuensi dari Inovasi, Konsep Pendidikan Berbasi Masyarakat, Discovery Learning, Project Based Learning, Pembelajaran Berbasis HOTS, Contextual Learning, Problem Based Learning dan Home Schooling.
Mobile call networks have been widely used to investigate communication patterns and the network of interactions of humans at the societal scale. Yet, more detailed analysis is often hindered by having no information about the nature of the relationships, even if some metadata about the individuals are available. Using a unique, large mobile phone database with information about individual surnames in a population in which people inherit two surnames: one from their father, and one from their mother, we are able to differentiate among close kin relationship types. Here we focus on the difference between the most frequently called alters depending on whether they are family relationships or not. We find support in the data for two hypotheses: (1) phone calls between family members are more frequent and last longer than phone calls between non-kin, and (2) the phone call pattern between family members show a higher variation depending on the stage of life-course compared to non-family members. We give an interpretation of these findings within the framework of evolutionary anthropology: kinship matters even when demographic processes, such as low fertility, urbanisation and migration reduce the access to family members. Furthermore, our results provide tools for distinguishing between different kinds of kin relationships from mobile call data, when information about names are unavailable.
Think tanks' role as development policy entrepreneurs and lobbyists is well recognised. Like NGOs, think tanks have also acted as classical intellectual labour cofounded by local and international agencies. This research examines organisational network of Indonesian think tanks. This study aims to understand the nature of networks of policy research organisations in Indonesia by investigating their policy networks, funding networks and coalition networks. Using network theory methodology, this paper maps and visualises the network of 187 Indonesian think tank organisations from 28 provinces in Indonesia. The research suggests that most think tank players in Indonesia target policy planning institutions to channel their policy research and inform development planning agendas. A significant amount of high-level policy research is associated with planning ministers and the line agencies such as respective ministers. The findings also show that most policy research organisations and national NGOs target the Indonesian parliament for policy advocacy and discourse. The findings also suggest that national NGOs and international donors remain influential in shaping national public policy networks.
Under Omni-media environment, Online Social Networks (OSN) have gradually become the most momentous platform for information propagation. Considering the interaction and coexistence of both positive and negative public opinion information (referred to as public opinion), it is of great significance for social development and economic stability to understand the co-evolution process of competitive public opinion and compress the spreading space of negative public opinion. Allowing for this point, this paper constructed a two-stage spreading model of competitive public opinion combing with the actual case of public opinion propagation, analysed the main factors influencing the co-evolution process, such as netizens’ intimacy, network literacy, and so on, and redefined netizens’ state transition probability matrix with the help of Markov process. Then, the effectiveness of the spreading model was verified and the propagation rule of public opinion was discussed in open and closed OSN through simulation experiments. Finally, the intervention strategies were proposed and optimised with the limitation of cost. The results show that the propagation of public opinion mainly depends on netizens’ behaviour with low literacy and presents difference characteristics in two types of OSN. During the intervention process of public opinion propagation, there exists an effective intervention interval and the best intervention strategy varies with the change of network topology. Our research provided a cornerstone for further understanding of the co-evolution process of competitive public opinion and the research conclusions also provided a certain decision-making reference for enterprises, governments and other regulators to reasonably respond to the propagation of public opinion.
Objectives:
To examine whether fragmentation of care is associated with worse in-hospital and 90-day outcomes following durable ventricular assist device (VAD) implant.
Study design:
Cohort study.
Methods:
This study was conducted using Medicare claims linked to the Society of Thoracic Surgeons (STS) Interagency Registry for Mechanically Assisted Circulatory Support (Intermacs) among patients undergoing VAD implant between July 2009 and April 2017. Medicare data were used to measure fragmentation of the multidisciplinary care delivery network for the treating hospital, based on providers' history of shared patients within the previous year. STS Intermacs data were used for risk adjustment and outcomes ascertainment. Hospitals were sorted into terciles based on the degree of network fragmentation, measured as the mean number of links separating providers in the network. Multivariable regression was used to associate network fragmentation with 90-day death or infection risk.
Results:
The cohort included 5159 patients who underwent VAD implant, with 11.2% dying and 27.6% experiencing an infection within 90 days after implant. After adjustment, a 1-unit increase in network fragmentation was associated with an increase of 0.179 in the probability of in-hospital infection and an increase of 0.183 in the probability of 90-day infection (both P < .05). Similar results were observed in models of the numbers of in-hospital and 90-day infections. Network fragmentation was predictive of the probability of 90-day mortality, although this relationship was not significant after adjustment.
Conclusions:
Care delivery network fragmentation is associated with higher in-hospital and 90-day infection rates following durable VAD implant. These networks may serve as novel targets for enhancing outcomes for patients undergoing VAD implant.
1) propose an im-proved version of the Erdös-Rényi (ER) the-ory of random networks to account for the scaling properties of a number of systems, including the link structure of the World Wide Web (WWW). The theory they present, however, is inconsistent with empirically ob-served properties of the Web link structure. Barabási and Albert write that because "of the preferential attachment, a vertex that acquires more connections than anoth-er one will increase its connectivity at a higher rate; thus, an initial difference in the connectivity between two vertices will in-crease further as the network grows. . . . Thus older . . . vertices increase their con-nectivity at the expense of the younger . . . ones, leading over time to some vertices that are highly connected, a 'rich-get-rich-er' phenomenon" [figure 2C of (1)]. It is this prediction of the Barabási-Albert (BA) model, however, that renders it unable to account for the power-law distribution of links in the WWW [figure 1B of (1)]. We studied a crawl of 260,000 sites, each one representing a separate domain name. We counted how many links the sites received from other sites, and found that the distribu-tion of links followed a power law (Fig. 1A). Next, we queried the InterNIC database (us-ing the WHOIS search tool at www. networksolutions.com) for the date on which the site was originally registered. Whereas the BA model predicts that older sites have more time to acquire links and gather links at a faster rate than newer sites, the results of our search (Fig. 1B) suggest no correlation between the age of a site and its number of links. The absence of correlation between age and the number of links is hardly surpris-ing; all sites are not created equal. An exciting site that appears in 1999 will soon have more links than a bland site created in 1993. The rate of acquisition of new links is probably proportional to the number of links the site already has, because the more links a site has, the more visible it becomes and the more new links it will get. (There should, however, be an additional propor-tionality factor, or growth rate, that varies from site to site.) Our recently proposed theory (2), which accounts for the power-law distribution in the number of pages per site, can also be applied to the number of links a site receives. In this model, the number of new links a site re-ceives at each time step is a random fraction of the number of links the site already has. New sites, each with a different growth rate, appear at an exponential rate. This model yields scatter plots similar to Fig. 1B, and can produce any power-law exponent 1.
Despite its increasing role in communication, the world wide web remains the least controlled medium: any individual or institution can create websites with unrestricted number of documents and links. While great efforts are made to map and characterize the Internet's infrastructure, little is known about the topology of the web. Here we take a first step to fill this gap: we use local connectivity measurements to construct a topological model of the world wide web, allowing us to explore and characterize its large scale properties. Comment: 5 pages, 1 figure, updated with most recent results on the size of the www
White "starter" persons in Los Angeles generated acquaintance chains to white and Negro target persons in New York, using the "small world method." The mean number of intermediaries between starters and target persons was similar to that found in earlier studies, approximately 5-6, and this remained constant over differences in race of the target person. The number of completed chains was 21/2 times as great for white targets as for Negro targets. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Systems as diverse as genetic networks or the world wide web are best
described as networks with complex topology. A common property of many large
networks is that the vertex connectivities follow a scale-free power-law
distribution. This feature is found to be a consequence of the two generic
mechanisms that networks expand continuously by the addition of new vertices,
and new vertices attach preferentially to already well connected sites. A model
based on these two ingredients reproduces the observed stationary scale-free
distributions, indicating that the development of large networks is governed by
robust self-organizing phenomena that go beyond the particulars of the
individual systems.
We study the statistical properties of a variety of diverse real-world networks. We present evidence of the occurrence of three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; (b) broad-scale networks, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and (c) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.
In a cell or microorganism, the processes that generate mass, energy, information transfer and cell-fate specification are seamlessly integrated through a complex network of cellular constituents and reactions. However, despite the key role of these networks in sustaining cellular functions, their large-scale structure is essentially unknown. Here we present a systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life. We show that, despite significant variation in their individual constituents and pathways, these metabolic networks have the same topological scaling properties and show striking similarities to the inherent organization of complex non-biological systems. This may indicate that metabolic organization is not only identical for all living organisms, but also complies with the design principles of robust and error-tolerant scale-free networks, and may represent a common blueprint for the large-scale organization of interactions among all cellular constituents.
The metabolic network of the catabolic, energy and biosynthetic metabolism of Escherichia coli is a paradigmatic case for the large genetic and metabolic networks that functional genomics efforts are beginning to elucidate. To analyse the structure of previously unknown networks involving hundreds or thousands of components by simple visual inspection is impossible, and quantitative approaches are needed to analyse them. We have undertaken a graph theoretical analysis of the E. coli metabolic network and find that this network is a small-world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans. Moreover, the connectivity of the metabolites follows a power law, another unusual but by no means rare statistical distribution. This provides an objective criterion for the centrality of the tricarboxylic acid cycle to metabolism. The small-world architecture may serve to minimize transition times between metabolic states, and contains evidence about the evolutionary history of metabolism.
Many communication and social networks have power-law link distributions, containing a few nodes that have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact that can be exploited when designing efficient search algorithms. We introduce a number of local search strategies that utilize high degree nodes in power-law graphs and that have costs scaling sublinearly with the size of the graph. We also demonstrate the utility of these strategies on the GNUTELLA peer-to-peer network.
We study the topology of e-mail networks with e-mail addresses as nodes and e-mails as links using data from server log files. The resulting network exhibits a scale-free link distribution and pronounced small-world behavior, as observed in other social networks. These observations imply that the spreading of e-mail viruses is greatly facilitated in real e-mail networks compared to random architectures.
This paper is an attempt to examine and define the world network of a typical individual by discovering how many of his or her acquaintances could be used as first steps in a small-world procedure, and for what reasons. The town and occupation of each target was provided, together with the ethnic background, where this could not be inferred from the name. Starters were instructed in the small-world experiment and asked to write down their choice, amongst the people they knew, for the first link in a potential chain from them to each of 1267 targets. Starters provided information on each choice made (e.g. mother, cousin, friend, acquaintance, etc.) together with the sex of the choice) and the reason that choice had been made. The reason could be in one or more of four categories: something about the location of the target caused the starter to think of his or her choice; the occupation of the target was responsible for the choice; the ethnicity of the target; or some other, unspecified, reason.
Arbitrarily selected individuals (N=296) in Nebraska and Boston are asked to generate acquaintance chains to a target person in Massachusetts, employing "the small world method" (Milgram, 1967). Sixty-four chains reach, the target person. Within this group the mean number of intermediaries between starters and targets is 5.2. Boston starting chains reach the target person with fewer intermediaries than those starting in Nebraska; subpopulations in the Nebraska group do not differ among themselves. The funneling of chains through sociometric "stars" is noted, with 48 per cent of the chains passing through three persons before reaching the target. Applications of the method to studies of large scale social structure are discussed.
Social networks have the surprising property of being “searchable”: Ordinary people are capable of directing messages through
their network of acquaintances to reach a specific but distant target person in only a few steps. We present a model that
offers an explanation of social network searchability in terms of recognizable personal identities: sets of characteristics
measured along a number of social dimensions. Our model defines a class of searchable networks and a method for searching
them that may be applicable to many network search problems, including the location of data files in peer-to-peer networks,
pages on the World Wide Web, and information in distributed databases.
Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
The small-world phenomenon - the principle that most of us are linked by
short chains of acquaintances - was first investigated as a question in
sociology and is a feature of a range of networks arising in nature and
technology. Experimental study of the phenomenon revealed that it has
two fundamental components: first, such short chains are ubiquitous, and
second, individuals operating with purely local information are very
adept at finding these chains. The first issue has been analysed, and
here I investigate the second by modelling how individuals can find
short chains in a large social network.
The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.
Using computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of collaboration between scientists in each of these disciplines. In these networks two scientists are considered connected if they have coauthored one or more papers together. We study a variety of statistical properties of our networks, including numbers of papers written by authors, numbers of authors per paper, numbers of collaborators that scientists have, existence and size of a giant component of connected scientists, and degree of clustering in the networks. We also highlight some apparent differences in collaboration patterns between the subjects studied. In the following paper, we study a number of measures of centrality and connectedness in the same networks.
Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
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