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Communicability reveals a transition to coordinated behavior in multiplex networks
Ernesto Estrada, Jesus Gomez-Gardenes
We analyse the flow of information in multiplex networks by means of the communicability function. First, we generalize this measure from its definition from simple graphs to multi…
About the Discriminant Power of the Subgraph Centrality and Other Centrality Measures About the Discriminant Power of the Subgraph Centrality and Other Centrality Measures(Working paper)
Ernesto Estrada
The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for whic…
On d-Walk Regular Graphs
Ernesto Estrada, Jose A. de la Pena
Let G be a graph with set of vertices 1,...,n and adjacency matrix A of size nxn. Let d(i,j)=d, we say that f_d:N->N is a d-function on G if for every pair of vertices i,j and k>=d…
Walk Entropies in Graphs
Ernesto Estrada, Jose A. de la Pena, Naomichi Hatano
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 statistical mechanics description of environmental variability in metabolic networks
Jonathan J Crofts, Ernesto Estrada
Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are high…
From Integer Sequences to Block Designs via Counting Walks in Graphs
Ernesto Estrada, José A. de la Peña
We define numbers of the type Oj(N) and Ej(N) and the corresponding integer sequences. We prove that these integer sequences, e.g., SO(N) and SE(N) correspond to the number of odd…