Distribution of components in the \(k\)-nearest neighbour random geometric graph for \(k\) below the connectivity threshold (Q388975)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distribution of components in the \(k\)-nearest neighbour random geometric graph for \(k\) below the connectivity threshold |
scientific article |
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Distribution of components in the \(k\)-nearest neighbour random geometric graph for \(k\) below the connectivity threshold (English)
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17 January 2014
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Consider a Poisson point process of intensity 1 in the plane. A random geometric graph \(G\) is defined on the set \(V\) of points of the process inside a square of area \(n\) by joining each point in \(V\) to its \(k\)-nearest neighbours in \(V\). The distribution of small connected components of \(G\) is studied for \(k=k(n)\) below the connectivity threshold. It is also shown that such components are in a specified sense not close together.
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Random geometric graphs
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Poisson process
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nearest neighbour, connected components
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