Abstract

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.

Abstract

We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long-standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation of the well-known configuration model in terms of an urn problem. Second, GHypEG allows incorporating arbitrary tendencies to connect different vertex pairs. Third, we present the closed-form expressions of the associated probability distribution ensures the analytical tractability of our formulation. This is in stark contrast with the previous state-of-the-art, which is to implement the configuration model by means of computationally expensive procedures.

Abstract

We introduce a statistical method to investigate the impact of dyadic relations on complex networks generated from repeated interactions. It is based on generalised hypergeometric ensembles, a class of statistical network ensembles developed recently. We represent different types of known relations between system elements by weighted graphs, separated in the different layers of a multiplex network. With our method we can regress the influence of each relational layer, the independent variables, on the interaction counts, the dependent variables. Moreover, we can test the statistical significance of the relations as explanatory variables for the observed interactions. To demonstrate the power of our approach and its broad applicability, we will present examples based on synthetic and empirical data.

Abstract

Statistical ensembles define probability spaces of all networks consistent with given aggregate statistics and have become instrumental in the analysis of relational data on networked systems. Their numerical and analytical study provides the foundation for the inference of topological patterns, the definition of network-analytic measures, as well as for model selection and statistical hypothesis testing. Contributing to the foundation of these important data science techniques, in this article we introduce generalized hypergeometric ensembles, a framework of analytically tractable statistical ensembles of finite, directed and weighted networks. This framework can be interpreted as a generalization of the classical configuration model, which is commonly used to randomly generate networks with a given degree sequence or distribution. Our generalization rests on the introduction of dyadic link propensities, which capture the degree-corrected tendencies of pairs of nodes to form edges between each other. Studying empirical and synthetic data, we show that our approach provides broad perspectives for community detection, model selection and statistical hypothesis testing.