Structural Inference of Hierarchies in Networks
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 realworld 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:physics/0610051
 Bibcode:
 2006physics..10051C
 Keywords:

 Physics  Physics and Society;
 Computer Science  Machine Learning;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 8 pages, 8 figures