Double gaussianization of graph spectra

Alhomaidhi, Alhanouf; Al-Thukair, Fawzi; Estrada, Ernesto

doi:10.1016/j.apm.2020.12.018

Cited by 1 publication

(3 citation statements)

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“…Two classical models, although not the only ones, to do such studies are the Erdős-Rényi random graphs [68] and the Barabási-Albert preferential attachment model [21]. For instance, the Estrada index of the network "neurons" studied here is E E (G real ) ≈ 1.3062 × 10 10 and that of an Erdős-Rényi random graph with the same number of nodes and edges is E E (G ER ) ≈ 3.4688×10 6 , which indicates that the large Estrada index of this network is not due to a random interconnection of the neurons of C. elegans. However, the consideration of a Barabási-Albert network with the same number of nodes and edges than those in the network "neurons" gives E E (G BA ) ≈ 1.2131 × 10 10 , which clearly points out that the relatively large Estrada index of this network may be explained by its skewed degree distribution.…”

Section: Random Graphsmentioning

confidence: 99%

“…The name Gaussian honors Carl Friedrich Gauss (1777-1855). 6 First we give a few general results for the Gaussian Estrada index (see [5,80]).…”

Section: Definition 20mentioning

confidence: 99%

“…They can be described in the current approach by the negative of two references eigenvalues λ1 and λ2 of the adjacency matrix. Then, we have the following [6] (Fig. 11).…”

Section: Double Gaussian Estrada Indexmentioning

confidence: 99%

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The many facets of the Estrada indices of graphs and networks

Estrada

2021

SeMA

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The Estrada index of a graph/network is defined as the trace of the adjacency matrix exponential. It has been extended to other graph-theoretic matrices, such as the Laplacian, distance, Seidel adjacency, Harary, etc. Here, we describe many of these extensions, including new ones, such as Gaussian, Mittag–Leffler and Onsager ones. More importantly, we contextualize all of these indices in physico-mathematical frameworks which allow their interpretations and facilitate their extensions and further studies. We also describe several of the bounds and estimations of these indices reported in the literature and analyze many of them computationally for small graphs as well as large complex networks. This article is intended to formalize many of the Estrada indices proposed and studied in the mathematical literature serving as a guide for their further studies.

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Section: Random Graphsmentioning

confidence: 99%

“…The name Gaussian honors Carl Friedrich Gauss (1777-1855). 6 First we give a few general results for the Gaussian Estrada index (see [5,80]).…”

Section: Definition 20mentioning

confidence: 99%