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| Full text | |
| Author(s): |
Martinez-Martinez, C. T.
[1, 2]
;
Mendez-Bermudez, J. A.
[2, 3]
;
Rodriguez, Jose M.
[4]
;
Sigarreta, Jose M.
[2, 5]
Total Authors: 4
|
| Affiliation: | [1] Univ Zaragoza, Inst Biocomputat & Phys Complex Syst BIFI, Zaragoza 50018 - Spain
[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 Carlos III Madrid, Dept Matemat, Ave Univ 30, Madrid 28911 - Spain
[5] Univ Autonoma Guerrero, Ctr Acapulco, Acapulco De Juarez 39610, Guerrero - Mexico
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | Applied Mathematics and Computation; v. 377, JUL 15 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
In this work we perform computational and analytical studies of the Randi ` c index R(G) in Erdos-Renyi models G(n, p) characterized by n vertices connected independently with probability p is an element of (0, 1). First, from a detailed scaling analysis, we show that <(R) over bar (G)> = < R(G)>/(n/2) scales with the product xi approximate to np, so we can define three regimes: a regime of mostly isolated vertices when xi< 0.01 (R(G) approximate to 0), a transition regime for 0.01 < xi < 10 (where 0 < R(G) < n/2), and a regime of almost complete graphs for xi > 10 (R(G) approximate to n/2). Then, motivated by the scaling of <(R) over bar (G)>, we analytically (i) obtain new relations connecting R(G) with other topological indices and characterize graphs which are extremal with respect to the relations obtained and (ii) apply these results in order to obtain inequalities on R (G) for graphs in Erdos-Renyi models. (C) 2020 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 19/06931-2 - Random matrix theory approach to complex networks |
| Grantee: | Francisco Aparecido Rodrigues |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |