Reciprocity, community detection, and link prediction in dynamic networks

Abstract

Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to model dynamic interactions. Particular interest has been devoted to extend the stochastic block model and its variant, to capture community structure as the network changes in time. While these models assume that edge formation depends only on the community memberships, recent work for static networks show the importance to include additional parameters capturing structural properties, as reciprocity for instance. Remarkably, these models are capable of generating more realistic network representations than those that only consider community membership. To this aim, we present a probabilistic generative model with hidden variables that integrates reciprocity and communities as structural information of networks that evolve in time. The model assumes a fundamental order in observing reciprocal data, that is an edge is observed, conditional on its reciprocated edge in the past. We deploy a Markovian approach to construct the network's transition matrix between time steps and parameters' inference is performed with an Expectation-Maximization algorithm that leads to high computational efficiency because it exploits the sparsity of the dataset. We test the performance of the model on synthetic dynamical networks, as well as on real networks of citations and email datasets. We show that our model captures the reciprocity of real networks better than standard models with only community structure, while performing well at link prediction tasks.

Inference of hyperedges and overlapping communities in hypergraphs

“…Such a condition could in principle be relaxed following the approaches of refs. 53 – 55 , we do not explore this here.…”

Anomaly detection and community detection in networks

“…As accurately identifying anomalies is deeply connected with the chosen null model determining what regular patterns are, it is important to consider other possible mechanism for tie formation, beyond community structure. In recent works [31][32][33], we found that modeling community patterns together with reciprocity effects, leads to higher predictive performance, thus more expressive generative models. This could significantly change the performance of our foundational model as well.…”

Link Prediction Model for Opportunistic Networks Based on Feature Fusion

“…Yasami Y et al [15] noted information that related to the dynamic features of node interactions, analyzed the properties of multilayer networks, and modeled the evolution of network topologies at different layers by an infinite factorial hidden Markov model of feature cascades. Safdari et al [16] noted the importance of additional parameters that captured structural properties. Therefore, they presented a probabilistic generative model that integrated these parameters and network communities as structural information.…”