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Book review: Darwinia
Summer reading: Spin
Runner
the Omnivoire's Delimma
the Golem's Eye |
Properties of highly clustered networks In this mathy paper, Newman presents a network model with tunable degree distributions and clustering coefficients. He analyzes the model to derive closed form solutions for the mean degree, percolation threshold (i.e., loosely and analogically speaking, this is the minimum infectiousness a disease must have to become an epidemic on the network), and the size of the giant component. Newman goes on to analyze epidemics in more detail using networks with both Poisson and power-law degree distributions. He finds that increased clustering decreases the total size of an epidemic but also decreases the epidemic threshold. In particular, no amount of clustering will produce a non-zero epidemic threshold in power-law degree distribution networks. Newman's model is simple: start with a bipartite graph of groups and individuals, project this down onto the individual graph only and connect individuals with probability p. Newman's insight (at least, I think it's his insight but I'm not a condensed matter physicist (even though I am made of condensed matter)) is that we can view this process as bond percolation. The rest, as they say, is math. This is an interesting paper though challenging. I'm still digesting it but if nothing else, it's another view of network models and their connections to physical processes. |
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