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# Common graphs and digraphs generators (Cython)

Common graphs and digraphs generators (Cython)

AUTHORS:

- David Coudert (2012)

`sage.graphs.graph_generators_pyx.``RandomGNP`(n, p, directed=False, loops=False)

  Returns a random graph or a digraph on \(n\) nodes. Each edge is inserted independently with probability \(p\).

  INPUTS:

  - `n` – number of nodes of the digraph
  - `p` – probability of an edge
  - `directed` – is a boolean indicating whether the random graph is directed or undirected (default).
  - `loops` – is a boolean set to True if the random digraph may have loops, and False (default) otherwise. This value is used only when `directed == True`.

  REFERENCES:

  [1] | Erdos and A. Renyi. On Random Graphs, Publ. Math. 6, 290 (1959).

  [2] | Gilbert. Random Graphs, Ann. Math. Stat., 30, 1141 (1959).

  EXAMPLE:

      sage: from sage.graphs.graph_generators_pyx import RandomGNP
      sage: set_random_seed(0)
      sage: D = RandomGNP(10, .2, directed = True)
      sage: D.num_verts()
      10
      sage: D.edges(labels=False)
      [(0, 2), (0, 5), (1, 5), (1, 7), (4, 1), (4, 2), (4, 9), (5, 0), (5, 2), (5, 3), (5, 7), (6, 5), (7, 1), (8, 2), (8, 6), (9, 4)]

  TESTS:

      sage: abs(mean([RandomGNP(200,.2).density() for i in range(30)])-.2) < .001
      True
      sage: RandomGNP(150,.2, loops = True)
      Traceback (most recent call last):
      ...
      ValueError: The 'loops' argument can be set to True only when 'directed' is True.

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