Network Models: Growth, Dynamics, and Failure

This paper reports on preliminary explorations, both empirical and analytical, of probabilistic models of large-scale networks. We first examine the structure of networks that grow by the addition of nodes and lines, using a class of connection rules motivated by considerations of distance and prior connectivity. Second, we examine the dynamic behavior of the binary influence model — a particular form of a more general model of networks in which each node has a status (for instance: normal, or failed) that behaves as a Markov chain, but with transitions that are influenced by the present status of each neighboring node. Some interesting influence model examples are analyzed, including one displaying a power-law relation between the frequency of a failure event and its extensiveness.