Quantifying Triadic Closure in Multi-Edge Social Networks

Multi-edge networks capture repeated interactions between individuals. In social networks, such edges often form closed triangles, or triads. Standard approaches to measure this triadic closure, however, fail for multi-edge networks, because they do not consider that triads can be formed by edges of different multiplicity. We propose a novel measure of triadic closure for multi-edge networks of social interactions based on a shared partner statistic. We demonstrate that our operalization is able to detect meaningful closure in synthetic and empirical multi-edge networks, where common approaches fail. This is a cornerstone in driving inferential network analyses from the analysis of binary networks towards the analyses of multi-edge and weighted networks, which offer a more realistic representation of social interactions and relations.Comment: 19 pages, 5 figures, 6 table

Clustering in complex networks. I. General formalism

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two --and not just one-- vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests new metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of the new formalism and the new metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the {\it weak} and the {\it strong transitivity} classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties

Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks

Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states.Comment: 21 pages, 10 figure

Topics in social network analysis and network science

This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recently, the majority involve only the most basic methods and thus scratch the surface of what might be accomplished. Cutting-edge methods using relevant examples and illustrations in health services research are provided

Unveiling homophily beyond the pool of opportunities

Unveiling individuals' preferences for connecting with similar others (choice homophily) beyond the structural factors determining the pool of opportunities, is a challenging task. Here, we introduce a robust methodology for quantifying and inferring choice homophily in a variety of social networks. Our approach employs statistical network ensembles to estimate and standardize homophily measurements. We control for group size imbalances and activity disparities by counting the number of possible network configurations with a given number of inter-group links using combinatorics. This method provides a principled measure of connection preferences and their confidence intervals. Our framework is versatile, suitable for undirected and directed networks, and applicable in scenarios involving multiple groups. To validate our inference method, we test it on synthetic networks and show that it outperforms traditional metrics. Our approach accurately captures the generative homophily used to build the networks, even when we include additional tie-formation mechanisms, such as preferential attachment and triadic closure. Results show that while triadic closure has some influence on the inference, its impact is small in homophilic networks. On the other hand, preferential attachment does not perturb the results of the inference method. We apply our method to real-world networks, demonstrating its effectiveness in unveiling underlying gender homophily. Our method aligns with traditional metrics in networks with balanced populations, but we obtain different results when the group sizes or degrees are imbalanced. This finding highlights the importance of considering structural factors when measuring choice homophily in social networks

Node-Centric Detection of Overlapping Communities in Social Networks

We present NECTAR, a community detection algorithm that generalizes Louvain method's local search heuristic for overlapping community structures. NECTAR chooses dynamically which objective function to optimize based on the network on which it is invoked. Our experimental evaluation on both synthetic benchmark graphs and real-world networks, based on ground-truth communities, shows that NECTAR provides excellent results as compared with state of the art community detection algorithms