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Predicting percolation thresholds in networks

Filippo Radicchi
Phys. Rev. E 91, 010801(R) – Published 15 January 2015
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Abstract

We consider different methods, which do not rely on numerical simulations of the percolation process, to approximate percolation thresholds in networks. We perform a systematic analysis on synthetic graphs and a collection of 109 real networks to quantify their effectiveness and reliability as prediction tools. Our study reveals that the inverse of the largest eigenvalue of the nonbacktracking matrix of the graph often provides a tight lower bound for true percolation threshold. However, in more than 40% of the cases, this indicator is less predictive than the naive expectation value based solely on the moments of the degree distribution. We find that the performance of all indicators becomes worse as the value of the true percolation threshold grows. Thus, none of them represents a good proxy for the robustness of extremely fragile networks.

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  • Received 19 November 2014

DOI:https://doi.org/10.1103/PhysRevE.91.010801

©2015 American Physical Society

Authors & Affiliations

Filippo Radicchi*

  • Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, Indiana 47405, USA

  • *filiradi@indiana.edu

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Issue

Vol. 91, Iss. 1 — January 2015

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