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Networks with the Smallest Average Distance and the Largest Average Clustering 
Abstract 
We describe the structure of the graphs wi … We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal. ore robust with respect to vertex removal. +


Authors  Dionysios Barmpoutis, Richard M Murray + 
ID  2010h + 
Source  arXiv, qbio.MN + 
Tag  bm10arxiv + 
Title  Networks with the Smallest Average Distance and the Largest Average Clustering + 
Type  Preprint + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:16:17 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/bm10arxiv.pdf + 
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