Entropy of random graph ensembles constrained with generalised degrees
Abstract
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph ensembles are used to quantify and compare topological properties of networks in a systematic and precise manner, using concepts from information theory. We calculate the Shannon entropy of random graph ensembles constrained with a specified generalised degree distribution. We find that the outcome has a natural connection with the degree-degree correlation which is implied by specifying a generalised degree distribution. We demonstrate how generalised degrees can be used to qualitatively and quantitatively describe a network.
Cite
@article{arxiv.1309.3645,
title = {Entropy of random graph ensembles constrained with generalised degrees},
author = {Ekaterina S. Roberts and Anthonius C. C. Coolen},
journal= {arXiv preprint arXiv:1309.3645},
year = {2013}
}
Comments
24 pages, 9 figures