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October 11, 2006

Hierarchy in networks

After several months of silence on it, I've finally posted a new paper (actually written more than 5 months ago!) on the arxiv about the hierarchical decomposition of network structure. I presented it at the 23rd International Conference on Machine Learning (ICML) Workshop on Social Network Analysis in June.

Aaron Clauset, Cristopher Moore, M. E. J. Newman, "Structural Inference of Hierarchies in Networks", to appear in Lecture Notes in Computer Science (Springer-Verlag). physics/0610051

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.

posted October 11, 2006 07:44 PM in Self Referential | permalink