Bond and site color-avoiding percolation in scale free networks.

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 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. An interesting form of critical behavior is found for networks with a power-law degree distribution independent of the number of colors, but still dependent on the existence of the colors and therefore different from standard percolation. Our percolation framework fills a gap between different multilayer network percolation scenarios.