Greedy routing and diameter bounds for small-world graphs are generalized from lattices to fixed-growth graphs of any dimensionality alpha, with an empirical application to U.S. road networks.
Firewalls, Disorder, and Percolation in Epidemics
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abstract
We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong disorder, i.e. a wide range of variation of susceptibility, patchiness in the spread of the epidemic is very likely, and the criterion for epidemic outbreak depends strongly on the disorder. These results are qualitatively different from those of standard models in epidemiology, but correspond to real effects.
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Fast Geographic Routing in Fixed-Growth Graphs
Greedy routing and diameter bounds for small-world graphs are generalized from lattices to fixed-growth graphs of any dimensionality alpha, with an empirical application to U.S. road networks.