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Abstract: We describe the structure of the graphs with the smallest average distanceand the largest average clustering given their order and size. There is usuallya unique graph with the largest average clustering, which at the same time hasthe smallest possible average distance. In contrast, there are many graphs withthe same minimum average distance, ignoring their average clustering. The formof these graphs is shown with analytical arguments. Finally, we measure thesensitivity to rewiring of this architecture with respect to the clusteringcoefficient, and we devise a method to make these networks more robust withrespect to vertex removal.



Author: Dionysios Barmpoutis, Richard M. Murray

Source: https://arxiv.org/







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