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. clustering ͉ graph ͉ likelihood I n the last few years, networks have found use in many fields as a powerful tool for representing the structure of complex systems (1-4). Metabolic, protein interaction, and genetic regulatory networks are now heavily studied in biology and medicine, the Internet and the world wide web in computer and information sciences, food webs and other species interaction networks in ecology, and networks of personal or social contacts in epidemiology, sociology, and the management sciences. The study of networks goes back much further than the current surge of interest in it, but recent work differs fundamentally from earlier studies in the sheer scale of the networks being analyzed. The networks studied 50 years ago by pioneers in the information and social sciences had, typically, a few dozen vertices and were small enough that they could easily be drawn on a piece of paper and perused for interesting features. In the 21st century, on the other hand, networks of thousands or millions of vertices are not unusual and network data on this scale cannot easily be represented in a way that allows quantitative analysis to be conducted by eye.
Newman and Leicht REF proposed a mixture model for exploring broad types of structure in networks.
Mixture models and exploratory analysis in networks
Proc. Natl. Acad. Sci. USA 104, 9564-9569 (2007)
Physics Medicine Computer Science