ArticlePDF Available

An Experimental Study of Search in Global Social Networks


Abstract and Figures

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.
Content may be subject to copyright.
An Experimental Study of Search
in Global Social Networks
Peter Sheridan Dodds,
Roby Muhamad,
Duncan J. Watts
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 ac-
counting 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 con-
clude that although global social networks are, in principle, searchable, actual
success depends sensitively on individual incentives.
It has become commonplace to assert that any
individual in the world can reach any other
individual through a short chain of social ties
(1, 2). Early experimental work by Travers
and Milgram (3) suggested that the average
length of such chains is roughly six, and
recent theoretical (4 ) and empirical (49)
work has generalized the claim to a wide
range of nonsocial networks. However, much
about this “small world” hypothesis is poorly
understood and empirically unsubstantiated.
In particular, individuals in real social net-
works have only limited, local information
about the global social network and, there-
fore, finding short paths represents a non-
trivial search effort (1012). Moreover, and
contrary to accepted wisdom, experimental
evidence for short global chain lengths is
extremely limited (13–15). For example,
Travers and Milgram report 96 message
chains (of which 18 were completed) initiated
by randomly selected individuals from a city
other than the target’s (3). Almost all other
empirical studies of large-scale networks
(49, 16 –19) have focused either on non-
social networks or on crude proxies of social
interaction such as scientific collaboration,
and studies specific to e-mail networks have
so far been limited to within single institu-
tions (20).
We have addressed these issues by con-
ducting a global, Internet-based social search
experiment (21). Participants registered on-
line (http://smallworld.sociology.columbia.
edu) and were randomly allocated one of 18
target persons from 13 countries (table S1).
Targets included a professor at an Ivy League
university, an archival inspector in Estonia, a
technology consultant in India, a policeman
in Australia, and a veterinarian in the Norwe-
gian army. Participants were informed that
their task was to help relay a message to their
allocated target by passing the message to a
social acquaintance whom they considered
“closer” than themselves to the target. Of the
98,847 individuals who registered, about
25% provided their personal information and
initiated message chains. Because subsequent
senders were effectively recruited by their
own acquaintances, the participation rate af-
ter the first step increased to an average of
37%. Including initial and subsequent send-
ers, data were recorded on 61,168 individuals
from 166 countries, constituting 24,163 dis-
tinct message chains (table S2). More than
half of all participants resided in North Amer-
ica and were middle class, professional,
college educated, and Christian, reflecting
commonly held notions of the Internet-using
population (22).
In addition to providing his or her chosen
contact’s name and e-mail address, each
sender was also required to describe how he
or she had come to know the person, along
with the type and strength of the resulting
relationship. Table 1 lists the frequencies
with which different types of relationships—
classified by type, origin, and strength—were
invoked by our population of 61,168 active
senders. When passing messages, senders
typically used friendships in preference to
business or family ties; however, almost half
of these friendships were formed through ei-
ther work or school affiliations. Furthermore,
successful chains in comparison with incom-
plete chains disproportionately involved pro-
fessional ties (33.9 versus 13.2%) rather than
friendship and familial relationships (59.8
versus 83.4%) (table S3). Successful chains
were also more likely to entail links that
originated through work or higher education
(65.1 versus 39.6%) (table S4). Men passed
messages more frequently to other men
(57%), and women to other women (61%),
and this tendency to pass to a same-sex con-
tact was strengthened by about 3% if the
target was the same gender as the sender and
similarly weakened in the opposite case. In-
dividuals in both successful and unsuccessful
chains typically used ties to acquaintances
they deemed to be “fairly close.” However, in
successful chains “casual” and “not close”
ties were chosen 15.7 and 5.9% more fre-
quently than in unsuccessful chains (table
S5), thus adding support, and some resolu-
tion, to the longstanding claim that “weak”
ties are disproportionately responsible for so-
cial connectivity (23).
Senders were also asked why they consid-
ered their nominated acquaintance a suit-
able recipient (Table 2). Two reasons—
geographical proximity of the acquaintance
to the target and similarity of occupation—
accounted for at least half of all choices, in
general agreement with previous findings
(24, 25). Geography clearly dominated the
early stages of a chain (when senders were
geographically distant) but after the third step
was cited less frequently than other charac-
teristics, of which occupation was the most
often cited. In contrast with previous claims
(3, 12), the presence of highly connected
individuals (hubs) appears to have limited
relevance to the kind of social search embod-
ied by our experiment (social search with
large associated costs/rewards or otherwise
modified individual incentives may behave
differently). Participants relatively rarely
nominated an acquaintance primarily because
he or she had many friends (Table 2,
“Friends”), and individuals in successful
Institute for Social and Economic Research and Pol-
icy, Columbia University, 420 West 118th Street,
New York, NY 10027, USA.
Department of Sociology,
Columbia University, 1180 Amsterdam Avenue, New
York, NY 10027, USA.
*To whom correspondence should be addressed. E-
Table 1. Type, origin, and strength of social ties used to direct messages. Only the top five categories in
the first two columns have been listed. The most useful category of social tie is medium-strength
friendships that originate in the workplace.
Type of relationship % Origin of relationship % Strength of relationship %
Friend 67 Work 25 Extremely close 18
Relatives 10 School/university 22 Very close 23
Co-worker 9 Family/relation 19 Fairly close 33
Sibling 5 Mutual friend 9 Casual 22
Significant other 3 Internet 6 Not close 4
chains were far less likely than those in in-
complete chains to send messages to hubs
(1.6 versus 8.2%) (table S6). We also find no
evidence of message funneling (3, 9)
through a single acquaintance of the target:
At most 5% of messages passed through a
single acquaintance of any target, and 95% of
all chains were completed through individu-
als who delivered at most three messages. We
conclude that social search appears to be
largely an egalitarian exercise, not one whose
success depends on a small minority of ex-
ceptional individuals.
Although the average participation rate
(about 37%) was high relative to those report-
ed in most e-mail based surveys (26 ), the
compounding effects of attrition over multi-
ple links resulted in exponential attenuation
of chains as a function of their length and
therefore an extremely low chain completion
rate (384 of 24,163 chains reached their
targets). Chains may have terminated (i)
randomly, because of individual apathy or
disinclination to participate (3, 27 ); (ii) pref-
erentially at longer chain lengths, corre-
sponding to the claim that chains get lostor
are otherwise unable to reach their targets (13);
or (iii) preferentially at short chain lengths,
because, for example, individuals nearer the
target are more likely to continue the chain.
Our findings support the random-failure
hypothesis for two reasons. First, with the
exception of the first step (which is special
because senders register rather than receive
a message from an acquaintance), the attri-
tion rate remains almost constant for all
chain lengths at which we have a sufficient-
ly large N; hence small confidence intervals
(Fig. 1A). Second, senders who did not
forward their messages after one week were
asked why they had not participated. Less
than 0.3% of those contacted claimed that
they could not think of an appropriate re-
cipient, suggesting that lack of interest or
incentive, not difficulty, was the main rea-
son for chain termination.
To estimate the reachability of all targets,
we first aggregate the 384 completed chains
across targets (Fig. 1B), finding the average
chain length to be L⬎⫽4.05. However,
this number is misleading because it repre-
sents an average only over the completed
chains, and shorter chains are more likely to
be completed. An ideal frequency distribu-
tion of chain lengths n(L) (i.e., the chain
lengths that would be observed in the hypo-
thetical limit of zero attrition) may be esti-
mated by accounting for observed attrition as
follows: n⬘共L) n(L)/
) (Fig.
1C, bars), where n(L) is the observed number
of chains completed after L steps (Fig. 1B)
and r
is the maximum-likelihood attrition
rate from step L to step L 1 (Fig. 1A,
circles). Using the observed values of r
have reconstructed the most likely ideal dis-
tribution n(L) (Fig. 1C, bars) under our as-
sumption of random attrition. Because the tail
of the distribution is poorly specified (owing
to the small number of observed chains at
large, L), we measure its median L
than its mean. We find L
7, and this can
be thought of as the typical ideal chain length
for a hypothetical average individual. By re-
peating the above procedure for chains that
started and ended in the same country (L
5) or in different countries (L
7), we can
disentangle to some extent the different un-
derlying distributions of chains, yielding an
estimated range of typical chain lengths 5
7, depending on the geographical sep-
aration of source and target.
Although the range of L
and the variation
in attrition rates across targets do not appear
great, the compounding effects of attrition
over the length of a message chain can nev-
ertheless generate large differences in mes-
sage completion rates. For example, a
decrease of 15% in attrition rates, when
compounded over the same ideal distribution
with L
6, can generate an 800% increase
in completion rate. The same attrition rates
[e.g., r
0.75, r
0.63 (L 1)], when
applied over chains with L
5 and 7,
respectively, can lead to completion rates that
vary by up to a factor of three.
Taken together, this evidence suggests a
mixed picture of search in global social net-
works. On the one hand, all targets may in
fact be reachable from random initial senders
in only a few steps, with surprisingly little
variation across targets in different countries
and professions. On the other hand, small
differences in either participation rates or the
underlying chain lengths can have a dramatic
impact on the apparent reachability of differ-
ent targets. Target 5 (a professor at a promi-
nent U.S. university) stands out in this re-
spect. Because 85% of senders were college
educated and more than half were American,
participants may have anticipated little diffi-
culty in reaching him, thus accounting for his
chainsattrition rate (54%) being much lower
than that of any other target (60 to 68%).
Target 5 received a notable 44% of all
completed chains, yet this result is consis-
tent with his true reachability being little
different from that of other targets; his
allocated senders may simply have been
more confident of success.
Our results therefore suggest that if indi-
viduals searching for remote targets do not
have sufficient incentives to proceed, the
small-world hypothesis will not appear to
hold (13), but that even a slight increase in
incentives can render social searches success-
Table 2. Reason for choosing next recipient. All quantities are percentages. Location, recipient is
geographically closer; Travel, recipient has traveled to target’s region; Family, recipient’s family originates
from target’s region; Work, recipient has occupation similar to target; Education, recipient has similar
educational background to target; Friends, recipient has many friends; Cooperative, recipient is considered
likely to continue the chain; Other, includes recipient as the target.
LNLocation Travel Family Work Education Friends Cooperative Other
1 19,718 33 16 11 16 3 9 9 3
2 7,414 40 11 11 19 4 6 7 2
3 2,834 37 8 10 26 6 6 4 3
4 1,014 33 6 7 31 8 5 5 5
5 349 27 3 6 38 12 6 3 5
6 117 21 3 5 42 15 4 5 5
73716 3 346 19 8 5 0
Fig. 1. Distributions of message chain lengths.
(A) Average per-step attrition rates (circles)
and 95% confidence interval (triangles). (B)
Histogram representing the number of chains
that are completed in L steps (L⬎⫽4.01).
(C) “Ideal” histogram of chain lengths recov-
ered from (B) by accounting for message attri-
tion (A). Bars represent the ideal histogram
recovered with average values of r [circles in
(A)] for the histogram in (B); lines represent a decomposition of the complete data into chains that
start in the same country as the target (circles) and those that start in a different country
8 AUGUST 2003 VOL 301 SCIENCE www.sciencemag.org828
ful under broad conditions. More generally,
the experimental approach adopted here sug-
gests that empirically observed network
structure can only be meaningfully inter-
preted in light of the actions, strategies, and
even perceptions of the individuals embed-
ded in the network: Network structure
alone is not everything.
References and Notes
1. I. de Sola Pool, M. Kochen, Soc. Networks 1, 1 (1978).
2. S. H. Strogatz, Nature 410, 268 (2001).
3. J. Travers, S. Milgram, Sociometry 32, 425 (1969).
4. D. J. Watts, S. H. Strogatz, Nature 393, 440 (1998).
5. R. Albert, H. Jeong, A.-L. Baraba´si, Nature 401, 130
6. L. A. Adamic, in Lecture Notes in Computer Science
1696, S. Abiteboul, A. Vercoustre, Eds. (Springer, Hei-
delberg, 1999), pp. 443– 454.
7. L. A. N. Amaral, A. Scala, M. Barthelemy, H. E. Stanley,
Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000).
8. A. Wagner, D. Fell, Proc. R. Soc. London, B 268, 1803
9. M. E. J. Newman, Phys. Rev. E 64, 016131 (2001).
10. J. Kleinberg, Nature 406, 845 (2000).
11. D. J. Watts, P. S. Dodds, M. E. J. Newman, Science 296,
1302 (2002).
12. L. A. Adamic, R. M. Lukose, A. R. Puniyani, B. A.
Huberman, Phys. Rev. E 64, 046135 (2001).
13. J. S. Kleinfeld, Society 39, 61 (2002).
14. C. Korte, S. Milgram, J. Pers. Soc. Psychol. 15, 101
15. N. Lin, P. Dayton, P. Greenwald, in Communication
Yearbook: Vol. 1, B. D. Ruben, Ed. (Transaction Books,
New Brunswick, NJ, 1977), pp. 107–119.
16. A.-L. Baraba´si, R. Albert, Science 286, 509 (1999).
17. M. Faloutsos, P. Faloutsos, C. Faloutsos, Comp.
Comm. Rev. 29, 251 (1999).
18. L. A. Adamic, B. A. Huberman, Science 287, 2115a
19. H. Jeong, B. Tombor, R. Albert, Z. N. Oltavi, A.-L.
Baraba´si, Nature 407, 651 (2000).
20. H. Ebel, L.-I. Mielsch, S. Bornholdt, Phys. Rev. E 66,
035103 (2002).
21. Materials and methods are available as supporting
material on Science Online.
22. W. Chen, J. Boase, B. Wellman, in The Internet in
Everyday Life, B. Wellman, C. Haythornthwaite, Eds.
(Blackwell, Oxford, 2002), pp. 74–113.
23. M. S. Granovetter, Am. J. Sociol. 78, 1360 (1973).
24. P. D. Killworth, H. R. Bernard, Soc. Networks 1, 159
25. H. R. Bernard, P. D. Killworth, M. J. Evans, C. McCarty,
G. A. Shelly, Ethnology 27, 155 (1988).
26. K. Sheehan, J. Comput. Mediated Commun. 6(2).
Available online at
issue2/sheehan.html (2001).
27. H. C. White, Soc. Forces 49(2), 259 (1970).
28. This research was supported in part by the National
Science Foundation, Intel Corporation, and Office of
Naval Research.
Supporting Online Material
Tables S1 to S6
2 December 2002; accepted 23 May 2003
Phylogenetics and the Cohesion
of Bacterial Genomes
Vincent Daubin,
Nancy A. Moran,
Howard Ochman
Gene acquisition is an ongoing process in many bacterial genomes, contributing
to adaptation and ecological diversification. Lateral gene transfer is considered
the primary explanation for discordance among gene phylogenies and as an
obstacle to reconstructing the tree of life. We measured the extent of phylo-
genetic conflict and alien-gene acquisition within quartets of sequenced ge-
nomes. Although comparisons of complete gene inventories indicate appre-
ciable gain and loss of genes, orthologs available for phylogenetic reconstruc-
tion are consistent with a single tree.
In all but the most reduced bacterial genomes,
there is a substantial fraction of genes whose
distributions and compositional features indi-
cate that they originated by lateral gene trans-
fer (LGT) (1). There is also clear evidence of
LGT between distantly related organisms
based on phylogenetic studies involving large
taxonomic samples (2). Given these findings,
incompatibility of phylogenies within and
among bacterial phyla based on different
genes has routinely been ascribed to LGT
(310). However, building molecular phylog-
enies for distantly related species is often a
difficult task, and choice of phylogenetic
methods, genes, or taxa can yield different
results. For example, there is still no consen-
sus on the monophyly of rodents (11, 12)or
the branching order of amniotes (13, 14 ), and
these groups are young compared to bacterial
phyla. In addition, distinguishing between or-
thologous genes (sequences that trace their
divergence to the splitting of organismal lin-
eages) and paralogous (duplicated) genes be-
comes increasingly difficult when consider-
ing more distantly related taxa.
The effects of LGT have been extended
from the deepest to the shallowest levels of
bacterial relationships. Indeed, the similar-
ities in gene sequence and gene content that
define widely accepted bacterial taxa have
been proposed to reflect boundaries to gene
transfer, rather than vertical transmission
and common organismal ancestry (10).
Thus, LGT may overwhelm attempts to
reconstruct the relationships among bacte-
rial taxa. The claim that the history of
bacteria might be more faithfully depicted
as a net than as a tree (7 ) relies upon the
postulate that the substantial incidence of
acquired DNA within genomes is the basis
for findings of phylogenetic incongruence
among genes. However, the genes detected
as recently transferred are, by and large,
different from those used to build species
phylogenies. The former are disproportion-
ately AT-rich, have restricted phyloge-
netic distributions, and usually encode ac-
cessory functions. In contrast, species phy-
logenies are based on genes with wide tax-
onomic distributions and having key roles
in cellular processes. However, such differ-
ences are often ignored when considering
the impact of LGT on bacterial relation-
ships. Although the incidence of recently
acquired DNA in bacterial genomes is the
most direct indication of extensive LGT
among species (1), the question of whether
the incongruence in gene phylogenies is
linked to the amount of new DNA in a
genome has not been addressed.
To investigate the relation between
DNA acquisition and phylogenetic incon-
gruence, we selected quartets of related,
sequenced genomes whose phylogenetic re-
lationships, based on small subunit ribo-
somal RNA (SSU rRNA) sequences, dis-
play the branching topology shown in Fig.
1. For each quartet, we inferred both the
number of recently acquired and lost genes
(based on their phylogenetic distributions)
and the proportion of ortholog phylogenies
supporting lateral transfers. We applied a
conservative method for identifying or-
thologs by including only those genes hav-
ing a single significant match per genome,
thus minimizing the risks of including hid-
den paralogs descending from within-ge-
nome duplication events. This contrasts
with the commonly used reciprocal best-
hit method (15) to infer orthology, which
can yield misleading results (16 ), especial-
ly when paralogs experience different evo-
lutionary rates. We retained all quartets of
species for which 25% of the genes from
the smallest genome were recovered as or-
thologs. We then tested which of the three
possible trees was significantly supported
for each ortholog family, using the Shimo-
daira-Hasegawa (SH) (17 ) test implement-
ed in Tree-puzzle 5.1 (18) at the 5% level
of significance (19). This method tests if an
alignment significantly supports a tree by
estimating the confidence limits of the like-
lihood estimates of the topologies.
Department of Biochemistry and Molecular Biophys-
Department of Ecology and Evolutionary Biology,
University of Arizona, Tucson, AZ, 85721, USA.
*To whom correspondence should be addressed. E-
... 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) ...
Full-text available
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.
... 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]. ...
Full-text available
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.
... Related work in computer science (Kleinberg, 2000), epidemiology (Keeling, 1999); and physics (Newman et al., 2001) all reveals how randomly placed long-distance links can influence social diffusion processes. Structural properties affect communication in (Albert et al., 1999); and (Dodds et al., 2003). Influence dynamics across virtual networks are discussed in (Backstrom et al., 2006). ...
Full-text available
We explore how macro and micro networks influence the diffusion of technological innovation and cultural/social behavior. Across the historical regimes in China and Europe, dynastic lordship's macro networks afforded different advantages in technological innovation. A network particular to Europe, the Roman Church, extended deep into local parishes with ethical norms prescribing fairness to strangers, and these cultural foundations helped guilds, trade associations, merchant courts, and universities operate cooperatively far beyond kinship. In contrast, Chinese emperors relied on ancient Confucian moral codes and system-spanning Confucian-educated officialdom; but fiscal limitations compelled officials to defer to local lineage orders, resulting in an enduring cultural pattern of guanxi and a polity whose institutional problem-solving capacity falter beyond the local level. Yet the civil service system has enabled China to outperform similar lineage-dependent regimes. Probing network topologies, we find that system-spanning networks can facilitate technological diffusion, but local networks influence cultural and behavioral change.
... Nearly all (99.3%) are separated by six or fewer. This is in line with classic findings on other human social networks (31)(32)(33)(34)(35)(36)(37)(38)(39). See Figure 4. ...
Full-text available
Bitcoin is a digital currency designed to rely on a decentralized, trustless network of anonymous agents. Using a pseudonymous-address-linking procedure that achieves >99% sensitivity and >99% specificity, we reveal that between launch (January 3rd, 2009), and when the price reached $1 (February 9th, 2011), most bitcoin was mined by only sixty-four agents. This was due to the rapid emergence of Pareto distributions in bitcoin income, producing such extensive resource centralization that almost all contemporary bitcoin addresses can be connected to these top agents by a chain of six transactions. Centralization created a social dilemma. Attackers could routinely exploit bitcoin via a "51% attack", making it possible for them to repeatedly spend the same bitcoins. Yet doing so would harm the community. Strikingly, we find that potential attackers always chose to cooperate instead. We model this dilemma using an N-player Centipede game in which anonymous players can choose to exploit, and thereby undermine, an appreciating good. Combining theory and economic experiments, we show that, even when individual payoffs are unchanged, cooperation is more frequent when the game is played by an anonymous group. Although bitcoin was designed to rely on a decentralized, trustless network of anonymous agents, its early success rested instead on cooperation among a small group of altruistic founders.
What are the implications of leading a research project related to different digital platforms ? There are some conceptual and methodological choices to make as well as technical hurdles to be aware of. To answer this question, central to research in information-communication, we present the practices developed during a research project related to crowdfunding. These practices aim to adapt our method to the standardisation of platforms and to the ethical foundations of social science research, such as anonymity and consent. Researchers process data produced by end-users in some context. This context is of paramount importance to interpret data without betraying the intentions of the subject producing them. The necessary skills for anonymising data sets are a matter of tinkering and require computer skills to overcome the shortcomings of the platforms. Eventually we would like to highlight that the ethical practices described in this paper often remain invisible and informal even though they condition the interpretation of the results and their reliability.
This book is a general introduction to the statistical analysis of networks, and can serve both as a research monograph and as a textbook. Numerous fundamental tools and concepts needed for the analysis of networks are presented, such as network modeling, community detection, graph-based semi-supervised learning and sampling in networks. The description of these concepts is self-contained, with both theoretical justifications and applications provided for the presented algorithms. Researchers, including postgraduate students, working in the area of network science, complex network analysis, or social network analysis, will find up-to-date statistical methods relevant to their research tasks. This book can also serve as textbook material for courses related to the statistical approach to the analysis of complex networks. In general, the chapters are fairly independent and self-supporting, and the book could be used for course composition “à la carte”. Nevertheless, Chapter 2 is needed to a certain degree for all parts of the book. It is also recommended to read Chapter 4 before reading Chapters 5 and 6, but this is not absolutely necessary. Reading Chapter 3 can also be helpful before reading Chapters 5 and 7. As prerequisites for reading this book, a basic knowledge in probability, linear algebra and elementary notions of graph theory is advised. Appendices describing required notions from the above mentioned disciplines have been added to help readers gain further understanding.
BACKGROUND Care fragmentation is associated with higher rates of infection after durable left ventricular assist device (LVAD) implant. Less is known about the relationship between care fragmentation and total spending, and whether this relationship is mediated by infections. METHODS Total payments were captured from admission to 180 days post-discharge. Drawing on network theory, a measure of care fragmentation was developed based on the number of shared patients among providers (ie, anesthesiologists, cardiac surgeons, cardiologists, critical care specialists, nurse practitioners, physician assistants) caring for 4,987 Medicare beneficiaries undergoing LVAD implantation between July 2009 - April 2017. Care fragmentation was measured using average path length, which describes how efficiently information flows among network members; longer path length indicates greater fragmentation. Terciles based on the level of care fragmentation and multivariable regression were used to analyze the relationship between care fragmentation and LVAD payments and mediation analysis was used to evaluate the role of post-implant infections. RESULTS The patient cohort was 81% male, 73% white, 11% Intermacs Profile 1 with mean (SD) age of 63.1 years (11.1). The mean (SD) level of care fragmentation in provider networks was 1.7 (0.2) and mean (SD) payment from admission to 180 days post-discharge was $246,905 ($109,872). Mean (SD) total payments at the lower, middle, and upper terciles of care fragmentation were $250,135 ($111,924), $243,288 ($109,376), and $247,290 ($108,241), respectively. In mediation analysis, the indirect effect of care fragmentation on total payments, through infections, was positive and statistically significant (β=16032.5, p=0.008). CONCLUSIONS Greater care fragmentation in the delivery of care surrounding durable LVAD implantation is associated with a higher incidence of infections, and consequently, higher payments for Medicare beneficiaries. Interventions to reduce care fragmentation may reduce the incidence of infections and in turn enhance the value of care for patients undergoing durable LVAD implantation.
In this paper, a two-layer network on various immunization strategies in the post-epidemic era is constructed and an improved symbiotic evolutionary model of COVID-19 and information collaboration is proposed. The dynamic transformation probability is introduced to influence the virus information transmission coevolutionary process. The dynamic transformation probability is influenced by the immunization strategies and vertex characteristics. We quantify the effects of immunization strategy, node properties, global temperature, and collaborative information dissemination on new crown outbreaks. We simulated our model in a scale-free network to analyze the propagation. The evolutionary phenomenon of the network during propagation was investigated. We simulated the proven epidemic information coevolutionary model in a two-layer network, validated it with real data comparisons by proving that our proposed model fits the real situation.
Full-text available
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. 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.
Full-text available
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
Full-text available
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.
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)
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.