Mixture models and exploratory analysis in networks

• Published in: Proceedings of the National Academy of Sciences - PNAS 2007-06, Vol.104 (23), p.9564-9569
• Main Authors: Newman, M.E.J, Leicht, E.A
• Format: Article
• Language: English
• Subjects: Adjectives; Algorithms; Communications networks; Community structure; Computational Biology - methods; Computer networking; Data Interpretation, Statistical; Data transmission; Friendship; Hyperlinks; Likelihood Functions; Mathematical models; Models, Theoretical; Nouns; Parametric models; Physical Sciences; Probability; Systems Biology - methods; Vertices
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.0610537104

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.