Walk Entropies in Graphs
Mathematical Physics
2013-07-03 v2 math.MP
Quantum Physics
Abstract
Entropies based on walks on graphs and on their line-graphs are defined. They are based on the summation over diagonal and off-diagonal elements of the thermal Green's function of a graph also known as the communicability. The walk entropies are strongly related to the walk regularity of graphs and line-graphs. They are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies. The temperature dependence of the walk entropies is also discussed. In particular, the walk entropy of graphs is shown to be non-monotonic for regular but non-walk-regular graphs in contrast to non-regular graphs.
Cite
@article{arxiv.1303.6203,
title = {Walk Entropies in Graphs},
author = {Ernesto Estrada and Jose A. de la Pena and Naomichi Hatano},
journal= {arXiv preprint arXiv:1303.6203},
year = {2013}
}
Comments
16 pages, 5 figures