2010/10/28 by Jianxi Gao, Sergey V. Buldyrev, Shlomo Havlin +1 · 1 citation
Physics and Astronomy · Computer Science · #physics.data-an #cs.SI #physics.soc-ph
paper · pdf · doi:10.1103/physrevlett.107.195701
published as Phys. Rev. Lett. 107, 195701 (2011) · 7 pages, 3 figures
arxiv created 2010/10/28 · arxiv updated 2011/11/09
Almost all network research has been focused on the properties of a single network that does not interact and depends on other networks. In reality, many real-world networks interact with other networks. Here we develop an analytical framework for studying interacting networks and present an exact percolation law for a network of n interdependent networks. In particular, we find that for n Erdős-Rényi networks each of average degree k, the giant component, P∞, is given by P∞=p[1-exp(-kP∞)]n where 1-p is the initial fraction of removed nodes. Our general result coincides for n=1 with the known Erdős-Rényi second-order phase transition for a single network. For any n ≥ 2 cascading failures occur and the transition becomes a first-order percolation transition. The new law for P∞ shows that percolation theory that is extensively studied in physics and mathematics is a limiting case (n=1) of a more general general and different percolation law for interdependent networks.