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TOLERANCE OF SCALE-FREE NETWORKS UNDER DEGREE SEGMENT PROTECTION AND REMOVAL

TAO FU

Experimental School, Beijing University of Technology at Tongzhou, Beijing 101101, China

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BO XU

Economics & Management School, Beihang University, Beijing 100191, China

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YONG-AN ZHANG

Economics and Management School, Beijing University of Technology, Beijing 100124, China

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YINI CHEN

Economics and Management School, Xi'an Technological University, Xi'an 710032, China

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https://doi.org/10.1142/S0217984912501564Cited by:0 (Source: Crossref)

Abstract

We study the tolerance of scale-free networks (following a power-law distribution P(k) = c⋅k^α) under degree segment protection and removal. We use percolation theory to examine analytically and numerically the critical node removal fraction p_c required for the disintegration of the network as well as the critical node protection fraction p_pc necessary to immunize the network against the disintegration. We show that when degree segment protection is prior to degree segment removal and 2 ≤ α ≤3, scale-free networks are quite robust due to the extremely low value of p_pc. Meanwhile, if we protect a degree segment with a fixed fraction of nodes, the threshold p_c has a generally downward trend as the degree sum of the segment decreases, but it is not strictly monotonic.

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