The communicability distance in graphs

Estrada, Ernesto (2012) The communicability distance in graphs. Linear Algebra and its Applications, 436 (11). pp. 4317-4328. ISSN 0024-3795 (https://doi.org/10.1016/j.laa.2012.01.017)

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Abstract

Let G be a simple connected graph with adjacency matrix A. The communicabilityGpq between two nodes p and q of the graph is defined as the pq-entry of G=exp(A). We prove here that ξp,q=(Gpp+Gqq-2Gpq)1/2 is a Euclidean distance and give expressions for it in paths, cycles, stars and complete graphs with n nodes. The sum of all communicabilitydistances in a graph is introduced as a new graph invariant ϒ(G). We compare this index with the Wiener and Kirchhoff indices of graphs and conjecture about the graphs with maximum and minimum values of this index.

ORCID iDs

Estrada, Ernesto ORCID logoORCID: https://orcid.org/0000-0002-3066-7418;
CORE (COnnecting REpositories)