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2012•Physical Review EOpen access

Degree correlations in random geometric graphs

Alberto Antonioni, Marco Tomassini

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Abstract

Spatially embedded networks are important in several disciplines. The prototypical spatial network we assume is the Random Geometric Graph, of which many properties are known. Here we present new results for the two-point degree correlation function in terms of the clustering coefficient of the graphs for two-dimensional space in particular, with extensions to arbitrary finite dimensions.

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What this paper is about

Spatially embedded networks are important in several disciplines. The prototypical spatial network we assume is the Random Geometric Graph, of which many properties are known. Here we present new results for the two-point degree correlation function in terms of the clustering coefficient of the graphs for two-dimensional space in particular, with extensions to arbitrary finite dimensions.

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Available abstract

Spatially embedded networks are important in several disciplines. The prototypical spatial network we assume is the Random Geometric Graph, of which many properties are known. Here we present new results for the two-point degree correlation function in terms of the clustering coefficient of the graphs for two-dimensional space in particular, with extensions to arbitrary finite dimensions.

Key concepts: Random graph, Clustering coefficient, Degree (music), Random geometric graph, Spatial network, Mathematics, Geometric networks, Geometric graph theory

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