Mixture models and exploratory analysis in networks

TLDR

Networks are widely used across biological, physical, and social sciences, yet understanding their structure remains a major challenge in complex systems research. The authors aim to develop a general technique for detecting structural features in large‑scale network data. The technique partitions nodes into classes with similar connection patterns, employing probabilistic mixture models and expectation‑maximization. Using these models, the authors show that the method can uncover a broad range of network structures without prior knowledge and illustrate its application to real‑world social and information networks.

Abstract

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding challenges in the study of complex systems. Here we describe a general technique for detecting structural features in large-scale network data that works by dividing the nodes of a network into classes such that the members of each class have similar patterns of connection to other nodes. Using the machinery of probabilistic mixture models and the expectation-maximization algorithm, we show that it is possible to detect, without prior knowledge of what we are looking for, a very broad range of types of structure in networks. We give a number of examples demonstrating how the method can be used to shed light on the properties of real-world networks, including social and information networks.