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Statistical Inference for Complex Networks Workshop, December 3-5, 2008, Santa Fe NM

Organizers: Aaron Clauset (SFI) and Cris Moore (UNM & SFI)

Aaron Clauset (homepage)

Hierarchically modular structure in complex networks

Many studies suggest that many complex networks exhibit not only modular structure, in which vertices divide into groups, but hierarchical structure, where these groups further subdivide into groups of groups, and so forth over multiple scales. In many cases these groups correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (protein interaction networks, metabolic networks, or genetic regulatory networks), or communities in social networks.

In this talk, we'll describe a generative model of hierarchical structure, and a general technique based on maximum likelihood for inferring such hierarchical structure directly from network data. We'll also show results indicating that hierarchies can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks, such as right-skewed degree distributions, high clustering coefficients, and short path lengths. As time allows, we'll discuss the prospect of using similar techniques to make other kinds of inferences about the large-scale organization of networks.

Joint work with Cristopher Moore (U. New Mexico and SFI) and Mark E.J. Newman (U. Michigan)