Network research has been focused on studying the properties of a single isolated
network, which rarely exists. We develop a general analytical framework for studying
percolation of n interdependent networks. We illustrate our analytical solutions for
three examples: (i) For any tree of n fully dependent Erdős-Rényi (ER) networks, each
of average degree k, we find that the giant component is P∞ =p[1-exp(-kP∞)](n) where
1-p is the initial fraction of removed nodes. This general result coincides for n
= 1 with the known second-order phase transition for a single network. For any n>1
cascading failures occur and the percolation becomes an abrupt first-order transition.
(ii) For a starlike network of n partially interdependent ER networks, P∞ depends
also on the topology-in contrast to case (i). (iii) For a looplike network formed
by n partially dependent ER networks, P∞ is independent of n.