The interplay of microscopic and mesoscopic structure in complex networks

TL;DR

This paper introduces an efficient probabilistic modeling approach that disentangles individual node and group contributions in complex networks, improving structure detection and statistical analysis accuracy.

Contribution

It presents a novel algorithm based on exponential random graph models and message passing to separate node and group effects in network data.

Findings

Enhanced detection of latent class structures in real data

Improved statistical significance assessment of network motifs

Successful prediction of gene-disease associations

Abstract

Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on unbiased generative probabilistic exponential random graph models and employing distributive message passing techniques, we present an efficient algorithm that allows one to separate the contributions of individual nodes and groups of nodes to the network structure. This leads to improved detection accuracy of latent class structure in real world data sets compared to models that focus on group structure alone. Furthermore, the inclusion of hitherto neglected group specific effects in models used to assess the statistical significance of small subgraph (motif) distributions in networks may be sufficient to explain most of the observed statistics. We show the predictive power of such generative models in forecasting putative gene-disease associations in the Online Mendelian Inheritance in Man (OMIM) database. The approach is suitable for both directed and undirected uni-partite as well as for bipartite networks.