Bond and site color-avoiding percolation in scale free networks

Kadović, Andrea; Krause, Sebastian M.; Caldarelli, Guido; Zlatić, Vinko (2018) Bond and site color-avoiding percolation in scale free networks. Physical Review E, 98 . ISSN 2470-0045

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

Abstract

Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one vulnerability (color), a robust color- avoiding connectivity is possible. However, many infrastructure networks show the problem of vulnerable classes of \textit{; ; ; ; edges}; ; ; ; instead of vertices. Here we formulate color- avoiding percolation for colored edges as well. Additionally, we allow for random failures of vertices or edges. The interplay of random failures and possible collective failures implies a rich phenomenology. A new form of critical behavior is found for networks with a power law degree distribution independent of the number of the colors, but still dependent on existence of the colors and therefore different from standard percolation. Our percolation framework fills a gap between different multilayer network percolation scenarios.

Item Type:

Article

Additional Information:

We want to express our gratitude to Anna Maria Loguericio for all the help during research, and to Antonio Scala, Caludio Conti, and Laura Pilozzi for all the fruitful discussions we had. V.Z. and G.C. acknowledge the Israel-Italian collaborative project NECST. A.K. and V.Z. acknowledge support by the H2020 CSA Twinning project No. 692194, "RBI-T-WINNING." V.Z. acknowledge partial support from Croatian centers of excellence Quantix-lie and Center of Excellence for Data Science and Cooperative Systems, and European Commission FET-Proactive project MULTIPLEX (Grant No. 317532). A.K. acknowledges the support of the Croatian Science Foundation.

Uncontrolled Keywords:

percolation ; complex network ; color graph ; avoiding vulnerabilities

Subjects:

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

Divisions:

Theoretical Physics Division

Projects:

Project title	Project leader	Project code	Project type
UNSPECIFIED	UNSPECIFIED	Israel-Italian collaborative project NECST	UNSPECIFIED
UNSPECIFIED	UNSPECIFIED	Cooperative Systems	UNSPECIFIED
UNSPECIFIED	UNSPECIFIED	Croatian centers of excellence Quantix-lie and Center of Excellence for Data Science	UNSPECIFIED
Ruđer Bošković Institute: Twinning for a step forward of the Theoretical Physics Division-RBI-T-WINNING	Fabrizio NESTI	692194	EK
Foundational Research on MULTIlevel comPLEX networks and systems-MULTIPLEX	UNSPECIFIED	317532	EK