Networks with arbitrary edge multiplicities
Abstract
One of the main characteristics of realworld networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of triangles in which edges, rather than vertices, participate. Here we show that the multiplicity distribution of real networks is in many cases scale free, and in general very broad. Thus, besides the fact that in real networks the number of edges attached to vertices often has a scalefree distribution, we find that the number of triangles attached to edges can have a scalefree distribution as well. We show that current models, even when they generate clustered networks, systematically fail to reproduce the observed multiplicity distributions. We therefore propose a generalized model that can reproduce networks with arbitrary distributions of vertex degrees and edge multiplicities, and study many of its properties analytically.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 January 2012
 DOI:
 10.1209/02955075/97/28005
 arXiv:
 arXiv:1101.2435
 Bibcode:
 2012EL.....9728005Z
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 EPL 97, 28005 (2012)