2021/11/30 by R. A. da Costa, G. J. Baxter, S. N. Dorogovtsev +2
Engineering · Physics and Astronomy · #Bioinformatics #Biology #Complex Network Analysis Techniques #Computational biology #Computer science #Data science #Gene #Genetics #Infrastructure Resilience and Vulnerability Analysis #Multiplex #Opinion Dynamics and Social Influence #Transition (genetics) #cond-mat.dis-nn #physics.soc-ph
paper · pdf · doi:10.1038/s41598-022-07913-x
published as Sci Rep 12, 3973 (2022) · 12 pages, 6 figures
openalex publication_date 2022/03/10 · arxiv created 2022/03/14 · arxiv updated 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, P(0)=0. Above a critical value of a control parameter, the removal of a tiny fraction Δ of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, Π=P(1). We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point Πc, respectively. In the limit Δ→0 the total collapse for Π>Πc takes a time T ∝ 1/(Π-Πc), while there is an exponential relaxation below Πc with a relaxation time τ∝ 1/[Πc-Π].