Homophily and Triadic Closure in Evolving Social Networks

We present a new network model accounting for homophily and triadic closure in the evolution of social networks. In particular, in our model, each node is characterized by a number of features and the probability of a link between two nodes depends on common features. The bipartite network of the actors and features evolves according to a dynamics that depends on three parameters that respectively regulate the preferential attachment in the transmission of the features to the nodes, the number of new features per node, and the power-law behavior of the total number of observed features. We provide theoretical results and statistical estimators for the parameters of the model. We validate our approach by means of simulations and an empirical analysis of a network of scientifc collaborations

Growing Attributed Networks through Local Processes

This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain the emergence of rich structural properties found in real-world networks. We make three contributions. First, we propose a parsimonious and accurate model of attributed network growth that jointly explains the emergence of in-degree distributions, local clustering, clustering-degree relationship and attribute mixing patterns. Second, our model is based on biased random walks and uses local processes to form edges without recourse to global network information. Third, we account for multiple sociological phenomena: bounded rationality, structural constraints, triadic closure, attribute homophily, and preferential attachment. Our experiments indicate that the proposed Attributed Random Walk (ARW) model accurately preserves network structure and attribute mixing patterns of six real-world networks; it improves upon the performance of eight state-of-the-art models by a statistically significant margin of 2.5-10x.Comment: 11 pages, 13 figure

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

The Problem of Action at a Distance in Networks and the Emergence of Preferential Attachment from Triadic Closure

In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of triangles. After a review of the concepts of triangle closing and preferential attachment, we present our argument, as well as a simplified model in which preferential attachment can be derived mathematically from triangle closing. Additionally, we perform experiments on synthetic graphs to demonstrate the emergence of preferential attachment in graph growth models based only on triangle closing.Comment: 13 pages, three 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

Partnership Ties Shape Friendship Networks: A Dynamic Social Network Study

Partnership ties shape friendship networks through different social forces. First, partnership ties drive clustering in friendship networks: individuals who are in a partnership tend to have common friends and befriend other couples. Second, partnership ties influence the level of homophily in these emerging friendship clusters. Partners tend to be similar in a number of attributes (homogamy). If one partner selects friends based on preferences for homophily, then the other partner may befriend the same person regardless of whether they also have homophilic preferences. Thus, two homophilic ties emerge based on a single partner's preferences. This amplification of homophily can be observed in many attributes (e.g., ethnicity, religion, age). Gender homophily, however, may be de-amplified, as the gender of partners differs in heterosexual partnerships. In our study, we follow dynamic friendship formation among 126 individuals and their cohabiting partners in a university-related graduate housing community over a period of nine months (N = 2,250 self-reported friendship relations). We find that partnership ties strongly shape the dynamic process of friendship formation. They are a main driver of local network clustering and explain a striking amount of homophil