ROBUSTNESS OF SCALE-FREE SPATIAL NETWORKS

• 成果类型: Article
• 署名作者: Jacob, Emmanuel; Morters, Peter
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Bath
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1098
• 发表日期: 2017
• 页码: 1680-1722
• 关键词: sublinear preferential attachment; models

摘要

A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the d-dimensional torus and are connected to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering, we can independently tune the power law exponent tau of the degree distribution and the rate -delta d at which the connection probability decreases with the distance of two vertices. We show that the network is robust if tau < 2 + 1/delta, but fails to be robust if tau > 3. In the case of one-dimensional space, we also show that the network is not robust if tau > 2 + 1/delta-1. This implies that robustness of a scale-free network depends not only on its power-law exponent but also on its clustering features. Other than the classical models of scale-free networks, our model is not locally treelike, and hence we need to develop novel methods for its study, including, for example, a surprising application of the BK-inequality.