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Infinite random graphs and properties of metrics
[chapter]

2016
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IMA Volumes in Mathematics and its Applications
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We give a survey of recent developments in the theory of countably infinite random geometric graphs. Classical results of Erdős and Rényi establish that countably infinite random graphs are isomorphic with probability 1. Infinite random graphs have vertices identified with points in a metric space, and edges are added with a given probability dependent on the relative location of their endpoints. The probability that infinite random geometric graphs are isomorphic is considered. The metric

doi:10.1007/978-3-319-24298-9_11
fatcat:44rsfbbm55hp3oawfhdxbhbd3u