Color-avoiding percolation

Krause, Sebastian M.; Danziger, Michael M.; Zlatić, Vinko (2017) Color-avoiding percolation. Physical Review E, 96 (2). ISSN 2470-0045

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Official URL: https://journals.aps.org/pre/abstract/10.1103/Phys...

Abstract

Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these vulnerabilities can greatly improve network robustness, if such paths exist. Color-avoiding percolation provides a theoretical framework for analyzing this scenario, focusing on the maximal set of nodes which can be connected via multiple color-avoiding paths. In this paper we extend the basic theory of color-avoiding percolation that was published in S. M. Krause et al. [Phys. Rev. X 6, 041022 (2016)]. We explicitly account for the fact that the same particular link can be part of different paths avoiding different colors. This fact was previously accounted for with a heuristic approximation. Here we propose a better method for solving this problem which is substantially more accurate for many avoided colors. Further, we formulate our method with differentiated node functions, either as senders and receivers, or as transmitters. In both functions, nodes can be explicitly trusted or avoided. With only one avoided color we obtain standard percolation. Avoiding additional colors one by one, we can understand the critical behavior of color-avoiding percolation. For unequal color frequencies, we find that the colors with the largest frequencies control the critical threshold and exponent. Colors of small frequencies have only a minor influence on color-avoiding connectivity, thus allowing for approximations.

Item Type:

Article

Additional Information:

We acknowledge financial support from the European Commission FET-Proactive project MULTIPLEX (Grant No. 317532) and the Italy-Israel NECSTproject. M.D. is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship. V.Z. acknowledges support by the H2020 CSA Twinning Project No. 692194, RBI-T-WINNING, and Croatian centers of excellence QuantixLie and Center of Research Excellence for Data Science and Cooperative Systems.

Uncontrolled Keywords:

Complex systems ; Continuous percolation transition ; Critical exponents ; Critical phenomena ; Network resilience ; Random graphs ; Technological networks ; Percolation theory

Subjects:

NATURAL SCIENCES > Physics
NATURAL SCIENCES > Physics > Condensed Matter Physics

Divisions:

Theoretical Physics Division

Projects: