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Computational Properties of General Indices on Random Networks

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Autor(es):
Aguilar-Sanchez, R. [1] ; Herrera-Gonzalez, I. F. [2] ; Mendez-Bermudez, J. A. [3, 4] ; Sigarreta, Jose M. [5]
Número total de Autores: 4
Afiliação do(s) autor(es):
[1] Benemerita Univ Autonoma Puebla, Fac Ciencias Quim, Puebla 72570 - Mexico
[2] Univ Popular Autonoma Estado Puebla, Dept Ingn, Puebla 72410 - Mexico
[3] Benemerita Univ Autonoma Puebla, Inst Fis, Apartado Postal J-48, Puebla 72570 - Mexico
[4] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[5] Univ Autonoma Guerrero, Fac Matemat, Carlos E Adame 54 Col Garita, Acapulco 39650 - Mexico
Número total de Afiliações: 5
Tipo de documento: Artigo Científico
Fonte: SYMMETRY-BASEL; v. 12, n. 8 AUG 2020.
Citações Web of Science: 0
Resumo

We perform a detailed (computational) scaling study of well-known general indices (the first and second variable Zagreb indices,M-1(alpha) (G) and M-2(alpha)(G), and the general sum-connectivity index, chi(alpha)(G)) as well as of general versions of indices of interest: the general inverse sum indeg index ISI alpha(G)and the general first geometric-arithmetic index GA(alpha)(G)(with alpha is an element of R). We apply these indices on two models of random networks: Erdos-Renyi (ER) random networksGER(nER,p)and random geometric (RG) graphs GRG(nRG,r). The ER random networks are formed bynERvertices connected independently with probability p is an element of{[}0,1]; while the RG graphs consist ofnRGvertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidean distance is less or equal than the connection radius r is an element of{[}0,2]. Within a statistical random matrix theory approach, we show that the average values of the indices normalized to the network size scale with the average degreekof the corresponding random network models, where k(ER)=(nER-1)pandkRG=(nRG-1)(pi r(2)-8r(3)/3+r(4)/2). That is X(GER)/n(ER)approximate to X(G(RG))/nRG if k(ER)=k(RG), with X representing any of the general indices listed above. With this work, we give a step forward in the scaling of topological indices since we have found a scaling law that covers different network models. Moreover, taking into account the symmetries of the topological indices we study here, we propose to establish their statistical analysis as a generic tool for studying average properties of random networks. In addition, we discuss the application of specific topological indices as complexity measures for random networks. (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