We make a graph representation of the microstructure of a complex material and then use network algorithms to identify co-operative geometric structures in these graphs. One well known co-operative geometric structure is the percolating backbone. We discuss two other structures which are of broader significance: The critical manifold and the optimal path. The definition and significance of these structures will be discussed. Results will be presented for the following problems: the grain boundary engineering of structural materials; the critical current of polycrystalline high temperature superconductors and; the onset voltage of polycrystalline varistors.
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