Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to a failure in another network. This in turn may cause further malfunction of additional nodes in the first network and so on. Such a cascade of failures, triggered by a failure of a small faction of nodes in only one network, may lead to the complete fragmentation of all networks. We introduce a model and an analytical framework for studying interdependent networks. We obtain interesting and surprising results that should significantly effect the design of robust real-world networks. For two interdependent Erdos-Renyi (ER) networks, we find that the critical average degree below which both networks collapse is <k_c>=2.445, compared to <k_c>=1 for a single ER network. Furthermore, while for a single network a broader degree distribution of the network nodes results in higher robustness to random failure, for interdependent networks, the broader the distribution is, the more vulnerable the networks become to random failure.
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