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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Topological versus spectral properties of random geometric graphs

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Autor(es):
Aguilar-Sanchez, R. [1] ; Mendez-Bermudez, J. A. [2, 3] ; Rodrigues, Francisco A. [3] ; Sigarreta, Jose M. [4]
Número total de Autores: 4
Afiliação do(s) autor(es):
[1] Benemerita Univ Autonoma Puebla, Fac Ciencias Quim, Puebla 72570 - Mexico
[2] Benemerita Univ Autonoma Puebla, Inst Fis, Apartado Postal J-48, Puebla 72570 - Mexico
[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[4] Univ Autonoma Guerrero, Fac Matemat, Carlos E Adame 54 Col Garita, Acapulco Gro 39650 - Mexico
Número total de Afiliações: 4
Tipo de documento: Artigo Científico
Fonte: Physical Review E; v. 102, n. 4 OCT 16 2020.
Citações Web of Science: 0
Resumo

In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs), a graph model used to study the structure and dynamics of complex systems embedded in a two-dimensional space. RGGs, G(n, l), consist of n vertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidian distance is less than or equal to the connection radius l is an element of {[}0, root 2]. To evaluate the topological properties of RGGs we chose two well-known topological indices, the Randic index R(G) and the harmonic index H(G). We characterize the spectral and eigenvector properties of the corresponding randomly weighted adjacency matrices by the use of random matrix theory measures: the ratio between consecutive eigenvalue spacings, the inverse participation ratios, and the information or Shannon entropies S(G). First, we review the scaling properties of the averaged measures, topological and spectral, on RGGs. Then we show that (i) the averaged-scaled indices, < R(G)> and < H(G)>, are highly correlated with the average number of nonisolated vertices < V-x(G)>; and (ii) surprisingly, the averaged-scaled Shannon entropy < S(G)> is also highly correlated with < V-x(G)>. Therefore, we suggest that very reliable predictions of eigenvector properties of RGGs could be made by computing topological indices. (AU)

Processo FAPESP: 19/06931-2 - Métodos de matrizes aleatórias em redes complexas
Beneficiário:Francisco Aparecido Rodrigues
Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional