The communicability distance in graphs

Ernesto Estrada

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)4317-4328
Number of pages12
JournalLinear Algebra and its Applications
Issue number11
Publication statusPublished - 1 Jun 2012


  • matrix functions
  • Euclidean distance
  • graph spectrum
  • graph distance
  • communicability

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