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Nonlinear Dynamics of Networks

CSIC Building (#406), Seminar Room 4122.

Explosive percolation in random graphs

Raissa D'Souza

University of California, Davis

Abstract:   Random graphs provide a framework for modeling network phenomena, especially phase transitions, such as the sudden emergence of large-scale connectivity. This talk will present a variant of the classic Erdos-Renyi model of network formation (using the power of two choices), showing that we can alter the location and also the nature of the phase transition, making for an explosive onset of connectivity. Next we develop random graph models of interacting networks, motivated by the fact that individual networks are increasingly interdependent (e.g., the Internet and the power grid, globalization of financial markets and of social networks). I show that interactions between different types of networks can actually lower the critical threshold, allowing large-scale connectivity to be achieved with fewer overall connections, with implications for the spread of disease across geographic regions and the design of simple communications networks.

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