Structural inference of hierarchies in networks

Authors:
Aaron Clauset;Cristopher Moore;Mark E. J. Newman
Affiliations:
Department of Computer Science, University of New Mexico, Albuquerque, NM;Department of Computer Science and Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM;Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI
Venue:
ICML'06 Proceedings of the 2006 conference on Statistical network analysis
Year:
2006

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Abstract

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of organization in the network. Here, we give a precise definition of hierarchical structure, give a generic model for generating arbitrary hierarchical structure in a random graph, and describe a statistically principled way to learn the set of hierarchical features that most plausibly explain a particular real-world network. By applying this approach to two example networks, we demonstrate its advantages for the interpretation of network data, the annotation of graphs with edge, vertex and community properties, and the generation of generic null models for further hypothesis testing.