Harman Patil (Editor)

Random geometric graph

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Random geometric graph httpsistackimgurcomFw8Rzpng

The evolution of the random geometric graph


In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according to a specified probability distribution) and connecting two nodes by a link if and only if their distance is in a given range, e.g. smaller than a certain neighborhood radius, r.

Contents

A real-world application of RGGs is the modeling of ad hoc networks.

Examples

  • In 1 dimension, one can study RGGs on a line of unit length (open boundary condition) or on a circle of unit circumference.
  • In 2 dimensions, an RGG can be constructed by choosing a flat unit square [0, 1] (see figure) or a torus of unit circumferences [0, 1)2 as the embedding space.

    • The simplest choice for the node distribution is to sprinkle them uniformly and independently in the embedding space.

    References

    Random geometric graph Wikipedia
    (Text) CC BY-SA


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