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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Muneer A. Sumour & F. W. S. Lima, 2017. "A systematic investigation of the gap in various Barabási–Albert and Erdös–Rényi networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(02), pages 1-10, February.
    • Handle: RePEc:wsi:ijmpcx:v:28:y:2017:i:02:n:s012918311750022x
    DOI: 10.1142/S012918311750022X
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