Far-out Vertices In Weighted Repeated Configuration Model

Bartlomiej Blaszczyszyn; Kumar Gaurav

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arXiv · 1209.2881

Far-out Vertices In Weighted Repeated Configuration Model

Bartlomiej Blaszczyszyn·Kumar Gaurav

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Abstract

We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the rest of the graph by a distance exceeding certain threshold play an important role in determining some global properties of the graph like diameter, flooding time etc., in spite of being statistically rare. We give a convergence result for the distribution of the number of such far-out vertices. We also make a conjecture about how this relates to the longest edge of the minimal spanning tree on the graph under consideration.

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Bartlomiej Blaszczyszyn, Kumar Gaurav. 2012-09-13. Far-out Vertices In Weighted Repeated Configuration Model. https://arxiv.org/abs/1209.2881

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