Percolation Transitions Are Not Always Sharpened by Making Networks Interdependent

• DOI: 10.1103/physrevlett.107.195702
• Publication Date: 2011-11-04T15:56:52Z
• Authors: Seung-Woo Son; Peter Grassberger; Maya Paczuski
• Keywords: Percolation (cognitive psychology); Interdependent networks; Discontinuity (linguistics); Exponent; Percolation Theory; Directed percolation

We study a model for coupled networks introduced recently by Buldyrev et al., [Nature (London) 464, 1025 (2010)], where each node has to be connected others via two types of links viable. Removing critical fraction nodes leads percolation transition that been claimed more abrupt than uncoupled networks. Indeed, it was found discontinuous in all cases studied. Using an efficient new algorithm we verify the is Erdös-Rényi networks, but find continuous fully interdependent diluted lattices. In 2 and 3 dimensions, order parameter exponent β larger ordinary percolation, showing less sharp, i.e., further from discontinuity, isolated Possible consequences spatially embedded are discussed.