A systematic investigation of the gap in various Barabási–Albert and Erdös–Rényi networks

Muneer A. Sumour () and F. W. S. Lima
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Muneer A. Sumour: Physics Department, Al-Aqsa University, P. O. Box 4051, Gaza, Gaza Strip, Palestinian Authority, Palestine
F. W. S. Lima: #x2020;Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64049-550, Teresina-PI, Brazil

International Journal of Modern Physics C (IJMPC), 2017, vol. 28, issue 02, 1-10

Abstract: On Barabási–Albert networks (BA) and variations as well as on Erdös–Rényi (ER) random graphs, we study the occurrence of a gap in the neighbor numbers k(i) versus node index i (with i=1,2,…,N) at m=2, 4, 6, 10, 50, 100 and 150 and with up to N=1000000 nodes. Here, we call “gap” a jump in the neighbor numbers k(i) when i equals the initial number m of neighbors; m is also the number of neighbors randomly selected by a newly added node. The size of the gap depends on the value of m and causes a deformation in the structure k(i) of the networks studied here. We give a systematic investigation of the gap in all types of BA networks known to us, and only the undirected BA (UBA) network and the ER graphs show no gap for m>4.

Keywords: Barabási–Albert networks; Erdös–Rényi graphs; directedness; gap (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S012918311750022X

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