2013/03/25 by Ernesto Estrada, Estrada, Ernesto, José Antonio de la Peña +3
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Network Analysis Techniques #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1303.6203
openalex publication_date 2013/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.