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Center for Nonlinear Studies |
Network reliability is the probability that a damaged network continues to function, given a model of the damage and a definition of what it means to "function". For many systems, the reliability is a monotonic polynomial in parameters of the damage model. There is a physical interpretation for the polynomial's coefficients, and, indeed, the polynomial itself is a partition function for the system. There is also a natural flow/cut interpretation. Together, these bring the power of decades of research in computer science and physics to bear on network analysis. It is well-known that evaluating the network reliability can be #P-hard. However, each coefficient can be estimated with an embarrassingly parallel Monte Carlo computation. What can we do with such estimates? Applications include renormalization group scaling, centrality statistics, tomography, and network classification. This talk will illustrate these uses with networks ranging from toys with a thousand edges to estimated social networks with several million edges.
Host: Aric Hagberg 5-4958