Internet Mathematics

The Structure of Geographical Threshold Graphs

Milan Bradonjić, Aric Hagberg, and Allon G. Percus

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We analyze the structure of random graphs generated by the geographical threshold model. The model is a generalization of random geometric graphs. Nodes are distributed in space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. We show how the degree distribution, percolation and connectivity transitions, clustering coefficient, and diameter relate to the threshold value and weight distribution. We give bounds on the threshold value guaranteeing the presence or absence of a giant component, connectivity and disconnectivity of the graph, and small diameter. Finally, we consider the clustering coefficient for nodes with a given degree $l$, finding that its scaling is very close to $1/l$ when the node weights are exponentially distributed.

Article information

Internet Math., Volume 5, Number 1-2 (2008), 113-140.

First available in Project Euclid: 25 November 2009

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Bradonjić, Milan; Hagberg, Aric; Percus, Allon G. The Structure of Geographical Threshold Graphs. Internet Math. 5 (2008), no. 1-2, 113--140.

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