Communicability in complex networks.

By Ernesto Estrada, Naomichi Hatano. Physical review. E, Statistical, nonlinear, and soft matter physics, 2007

621 citations recorded by the source corpus.

We propose a new measure of the communicability of a complex network, which is a broad generalization of the concept of the shortest path. According to the new measure, most of the real-world networks display the largest communicability between the most connected (popular) nodes of the network (assortative communicability). There are also several networks with the disassortative communicability, where the most "popular" nodes communicate very poorly to each other. Using this information we classify a diverse set of real-world complex systems into a small number of universality classes based on their structure-dynamic correlation. In addition, the new communicability measure is able to distinguish finer structures of networks, such as communities into which a network is divided. A community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of the nodes in the network.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dc3b54afc1e8475b2a8d8de148c2dbe6d8800c37

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Citations in the corpus

A map of abstract relational knowledge in the human hippocampal–entorhinal cortex (2017, background): “Graph theory also proposes a second measure that is closely related, the matrix exponential (Estrada and Hatano, 2008, 2010): eA ¼ X¥ n¼0 An n!”
Communication dynamics in complex brain networks (2017, background): “The graph measure called communicability 104 operates under this hypothesis, offering an upper bound on the parallel processing capacity of the system, as all elements take part in signal transfer.”
Quadrature rule-based bounds for functions of adjacency matrices (2010, methodology): “Some of these quantities are expressed in terms of adjacency matrices; in particular, we will use here thenotions of Estrada index, subgraph centrality and communicability, which are presented indetail in [5,8–16]; see also the discussion in [20].”
The Kuramoto model in complex networks (2015, background): “For instance, the concept of “centrality” can be related to the average shortest distances [147], network spectra [442] and random walks [443].”
The communicability distance in graphs (2012, background): “The communicability between the nodes p and q in G has been defined as a weighted sum of all walks starting at node p and ending at node q, in which the weighting scheme gives more weight to the shortest walks than to the longer ones [1].”
The Physics of Communicability in Complex Networks (2011, methodology): “Then, overlapped communities are identified as the cliques of this graph (Estrada and Hatano, 2008; 2009a).”
The structure and dynamics of multilayer networks (2014, background): “Another important measure (when dealing with RWs) is the concept of communicability [216,217], that quantifies the number of possible paths communicating twogivennodes of a network.”
Cliques and cavities in the human connectome (2016, background): “Ci,j = (exp(D−1/2AD−1/2))ij with D := diag(si) for si the strength of node i in the adjacency matrix A, providing a normalization step where each aij is divided by √ didj (Crofts and Higham 2009; Estrada and Hatano 2008).”
Community detection in graphs (2009, background): “Another possibility, suggested by Estrada and Hatano [89,90], is to weigh paths of length l with the inverse factorial 1/l!.”
Complex network measures of brain connectivity: Uses and interpretations (2010, background): “Note that measures such as the characteristic path length and the global ef ﬁ ciency do not incorporate multiple and longer paths, which may signi ﬁ cantly contribute to integration in larger and sparser networks ( Estrada and Hatano, 2008).”
Closures and Cavities in the Human Connectome (2016, background): “[23] Ernesto Estrada and Naomichi Hatano.”
Network Properties Revealed through Matrix Functions (2010, background): “Estrada and Hatano [29] interpreted the subgraph centrality measure defined in (5) from the viewpoint of statistical mechanics and showed that it may be regarded as a partition function for the network.”
Mapping neurotransmitter systems to the structural and functional organization of the human neocortex (2021, background): “Communicability is defined as the weighted average of all walks and paths between two brain regions, and represents diffusive communication [33].”
Multilayer networks (2013, background): “The ability to define generalizations of such concepts for multilayer networks yields natural extensions of many other measures for monoplex networks — including graph distance, connected components, betweenness centralities, random walks, communicability [117], and clustering coefficients.”