Dane Taylor, Daniel B. Larremore
Formation and fragmentation of networks is typically studied using percolation theory, but most previous research has been restricted to studying a phase transition in cluster size, examining the emergence of a giant component. This approach does not address the effects of evolving network structure on dynamics that may occur at the nodes, such as synchronization of oscillators or epidemic spreading. We introduce new link-formation rules, called Social Climber attachment, that may be combined with arbitrary percolation models to produce a previously unstudied phase transition using the largest eigenvalue of the network adjacency matrix as the order parameter, a measure of "connectivity," chosen due to its significance in analyses of many network-coupled dynamical systems. We provide analysis and discuss implications for controlling dynamics on networks.
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http://arxiv.org/abs/1205.3832
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