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# random_geometric_graph

random_geometric_graph(n, radius, dim=2, pos=None, p=2, seed=None, *, pos_name='pos')

  Returns a random geometric graph in the unit cube of dimensions `dim`.

  The random geometric graph model places `n` nodes uniformly at random in the unit cube. Two nodes are joined by an edge if the distance between the nodes is at most `radius`.

  Edges are determined using a KDTree when SciPy is available. This reduces the time complexity from \(O(n^2)\) to \(O(n)\).

  Parameters:
    n int or iterable

      Number of nodes or iterable of nodes

    radius: float

      Distance threshold value

    dim int, optional

      Dimension of graph

    pos dict, optional

      A dictionary keyed by node with node positions as values.

    p float, optional

      Which Minkowski distance metric to use. `p` has to meet the condition `1 <= p <= infinity`.

      If this argument is not specified, the \(L^2\) metric (the Euclidean distance metric), p = 2 is used. This should not be confused with the `p` of an Erdős-Rényi random graph, which represents probability.

    seed integer, random_state, or None (default)

      Indicator of random number generation state. See Randomness.

    pos_name string, default=”pos”

      The name of the node attribute which represents the position in 2D coordinates of the node in the returned graph.

  Returns:
    Graph

      A random geometric graph, undirected and without self-loops. Each node has a node attribute `'pos'` that stores the position of that node in Euclidean space as provided by the `pos` keyword argument or, if `pos` was not provided, as generated by this function.

  Notes

  This uses a k-d tree to build the graph.

  The `pos` keyword argument can be used to specify node positions so you can create an arbitrary distribution and domain for positions.

  For example, to use a 2D Gaussian distribution of node positions with mean (0, 0) and standard deviation 2:

      >>> import random
      >>> n = 20
      >>> pos = {i: (random.gauss(0, 2), random.gauss(0, 2)) for i in range(n)}
      >>> G = nx.random_geometric_graph(n, 0.2, pos=pos)

  References

  [1]

  Penrose, Mathew, Random Geometric Graphs, Oxford Studies in Probability, 5, 2003.

  Examples

  Create a random geometric graph on twenty nodes where nodes are joined by an edge if their distance is at most 0.1:

      >>> G = nx.random_geometric_graph(20, 0.1)