Hidden transition in multiplex networks

Complexity Digest

R. A. da Costa, G. J. Baxter, S. N. Dorogovtsev, J. F. F. Mendes
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…

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