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The relevance of higher-order ties

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Abstract

Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperlinks) of different sizes to the overall network structure. Yet, this has many important applications, especially when the network has meaningful node labels. In this work, we propose a comprehensive methodology to precisely measure the contribution of different orders to the overall network structure. First, we propose the order contribution measure, which quantifies the contribution of hyperlinks of different orders to the link weights (local scale), number of triangles (mesoscale) and size of the largest connected component (global scale) of the pairwise weighted network. Second, we propose the measure of order relevance, which gives insights in how hyperlinks of different orders contribute to the considered network property. Most interestingly, it enables an assessment of whether this contribution is synergistic or redundant with respect to that of hyperlinks of other orders. Third, to account for labels, we propose a metric of label group balance to assess how hyperlinks of different orders connect label-induced groups of nodes. We applied these metrics to a large-scale board interlock network and scientific collaboration network, in which node labels correspond to geographical location of the nodes. Experiments including a comparison with randomized null models reveal how from the global level perspective, we observe synergistic contributions of orders in the board interlock network, whereas in the collaboration network there is more redundancy. The findings shed new light on social scientific debates on the role of busy directors in global business networks and the connective effects of large author teams in scientific collaboration networks.

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Protein–protein interactions are crucial in many biological pathways and facilitate cellular function. Investigating these interactions as a graph of pairwise interactions can help to gain a systemic understanding of cellular processes. It is known, however, that proteins interact with each other not exclusively in pairs but also in polyadic interactions and that they can form multiprotein complexes, which are stable interactions between multiple proteins. In this manuscript, we use hypergraphs to investigate multiprotein complex data. We investigate two random null models to test which hypergraph properties occur as a consequence of constraints, such as the size and the number of multiprotein complexes. We find that assortativity, the number of connected components, and clustering differ from the data to these null models. Our main finding is that projecting a hypergraph of polyadic interactions onto a graph of pairwise interactions leads to the identification of different proteins as hubs than the hypergraph. We find in our data set that the hypergraph degree is a more accurate predictor for gene essentiality than the degree in the pairwise graph. In our data set analysing a hypergraph as pairwise graph drastically changes the distribution of the local clustering coefficient. Furthermore, using a pairwise interaction representing multiprotein complex data may lead to a spurious hierarchical structure, which is not observed in the hypergraph. Hence, we illustrate that hypergraphs can be more suitable than pairwise graphs for the analysis of multiprotein complex data.
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The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Kuramoto model which describes the interactions between oscillators placed not only on nodes but also on links, triangles, and so on. We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.
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Multibody interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear, regardless of the underlying multibody structure. As a practical application, we introduce a specific nonlinear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure, and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarized clusters where multibody interactions make one cluster dominate the other.
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Network data on connections between corporate actors and entities – for instance through co-ownership ties or elite social networks – are increasingly available to researchers interested in probing the many important questions related to the study of modern capitalism. Given the analytical challenges associated with the nature of the subject matter, variable data quality and other problems associated with currently available data on this scale, we discuss the promise and perils of using big corporate network data (BCND). We propose a standard procedure for helping researchers deal with BCND problems. While acknowledging that different research questions require different approaches to data quality, we offer a schematic platform that researchers can follow to make informed and intelligent decisions about BCND issues and address these through a specific work-flow procedure. For each step in this procedure, we provide a set of best practices for how to identify, resolve and minimize the BCND problems that arise.
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The tremendous diversity of species in ecological communities has motivated a century of research into the mechanisms that maintain biodiversity. However, much of this work examines the coexistence of just pairs of competitors. This approach ignores those mechanisms of coexistence that emerge only in diverse competitive networks. Despite the potential for these mechanisms to create conditions under which the loss of one competitor triggers the loss of others, we lack the knowledge needed to judge their importance for coexistence in nature. Progress requires borrowing insight from the study of multitrophic interaction networks, and coupling empirical data to models of competition.
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Nowadays, social networks of ever increasing size are studied by researchers from a range of disciplines. The data underlying these networks is often automatically gathered from API's, websites or existing databases. As a result, the quality of this data is typically not manually validated, and the resulting networks may be based on false, biased or incomplete data. In this paper, we investigate the effect of data quality issues on the analysis of large networks. We focus on the global board interlock network, in which nodes represent firms across the globe, and edges model social ties between firms -- shared board members holding a position at both firms. First, we demonstrate how we can automatically assess the completeness of a large dataset of 160 million firms, in which data is missing not at random. Second, we present a novel method to increase the accuracy of the entries in our data. By comparing the expected and empirical characteristics of the resulting network topology, we develop a technique that automatically prunes and merges duplicate nodes and edges. Third, we use a case study of the board interlock network of Sweden to show how poor quality data results in incorrect network topologies, biased centrality values and abnormal influence spread under a well-known diffusion model. Finally, we demonstrate how our data quality assessment methods help restore the correct network structure, ultimately allowing us to derive meaningful and correct results from analyzing the network.
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Significance We study the dynamic network of real world person-to-person interactions between approximately 1,000 individuals with 5-min resolution across several months. There is currently no coherent theoretical framework for summarizing the tens of thousands of interactions per day in this complex network, but here we show that at the right temporal resolution, social groups can be identified directly. We outline and validate a framework that enables us to study the statistical properties of individual social events as well as series of meetings across weeks and months. Representing the dynamic network as sequences of such meetings reduces the complexity of the system dramatically. We illustrate the usefulness of the framework by investigating the predictability of human social activity.
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The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling - including three and four-way interactions of the oscillator phases - that appears generically at the next order in normal-form based calculations, can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
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What impact did the recent financial crisis have on the corporate elite's international network? Has corporate governance taken on an essentially national structure or have transnational networks remained robust? We investigate this issue by comparing the networks of interlocking directorates among the 176 largest corporations in the world economy in 1976, 1996, 2006 and 2013. We find that corporate elites have not retrenched into their national business communities: the transnational network increased in relative importance and remained largely intact during the crisis lasting from 2006 to 2013. However, this network does not depend - as it used to do - on a small number of big linkers but on a growing number of single linkers. The network has become less hierarchical. As a group, the corporate elite has become more transnational in character. We see this as indicative of a recomposition of the corporate elite from a national to a transnational orientation.
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A key debate on the merits and consequences of globalisation asks to what extent we have moved to a multipolar global political economy. Here we investigate this issue through the properties and topologies of corporate elite networks and ask: what is the community structure of the global corporate elite? In order to answer this question, we analyse how the largest one million firms in the world are interconnected at the level of corporate governance through interlocking directorates. Community detection through modularity maximisation reveals that regional clusters play a fundamental role in the network architecture of the global political economy. Transatlantic connections remain particularly strong: Europe and North America remain interconnected in a dense network of shared directors. A distinct Asian cluster stands apart as separate and oriented more towards itself. While it develops and gains economic and political power, Asia remains by and large outside the scope of the networks of the incumbent global (that is, North Atlantic) corporate elite. We see this as a sign of the rise of competing corporate elites. But the corporate elites from the traditional core countries still form a powerful opponent for any competing faction in the global corporate elite.
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This paper provides the first historical analysis of the relationship between collaboration and scientific impact, using three indicators of collaboration (number of authors, number of addresses, and number of countries) and including articles published between 1900 and 2011. The results demonstrate that an increase in the number of authors leads to an increase in impact--from the beginning of the last century onwards--and that this is not simply due to self-citations. A similar trend is also observed for the number of addresses and number of countries represented in the byline of an article. However, the constant inflation of collaboration since 1900 has resulted in diminishing citation returns: larger and more diverse (in terms of institutional and country affiliation) teams are necessary to realize higher impact. The paper concludes with a discussion of the potential causes of the impact gain in citations of collaborative papers.