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"""
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Generators for random intersection graphs.
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"""
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import networkx as nx
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from networkx.utils import py_random_state
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__all__ = [
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"uniform_random_intersection_graph",
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"k_random_intersection_graph",
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"general_random_intersection_graph",
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]
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@py_random_state(3)
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@nx._dispatchable(graphs=None, returns_graph=True)
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def uniform_random_intersection_graph(n, m, p, seed=None):
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"""Returns a uniform random intersection graph.
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Parameters
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----------
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n : int
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The number of nodes in the first bipartite set (nodes)
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m : int
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The number of nodes in the second bipartite set (attributes)
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p : float
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Probability of connecting nodes between bipartite sets
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seed : integer, random_state, or None (default)
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Indicator of random number generation state.
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See :ref:`Randomness<randomness>`.
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See Also
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--------
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gnp_random_graph
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References
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----------
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.. [1] K.B. Singer-Cohen, Random Intersection Graphs, 1995,
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PhD thesis, Johns Hopkins University
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.. [2] Fill, J. A., Scheinerman, E. R., and Singer-Cohen, K. B.,
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Random intersection graphs when m = !(n):
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An equivalence theorem relating the evolution of the g(n, m, p)
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and g(n, p) models. Random Struct. Algorithms 16, 2 (2000), 156–176.
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"""
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from networkx.algorithms import bipartite
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G = bipartite.random_graph(n, m, p, seed)
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return nx.projected_graph(G, range(n))
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@py_random_state(3)
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@nx._dispatchable(graphs=None, returns_graph=True)
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def k_random_intersection_graph(n, m, k, seed=None):
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"""Returns a intersection graph with randomly chosen attribute sets for
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each node that are of equal size (k).
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Parameters
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----------
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n : int
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The number of nodes in the first bipartite set (nodes)
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m : int
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The number of nodes in the second bipartite set (attributes)
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k : float
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Size of attribute set to assign to each node.
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seed : integer, random_state, or None (default)
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Indicator of random number generation state.
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See :ref:`Randomness<randomness>`.
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See Also
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--------
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gnp_random_graph, uniform_random_intersection_graph
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References
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----------
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.. [1] Godehardt, E., and Jaworski, J.
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Two models of random intersection graphs and their applications.
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Electronic Notes in Discrete Mathematics 10 (2001), 129--132.
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"""
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G = nx.empty_graph(n + m)
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mset = range(n, n + m)
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for v in range(n):
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targets = seed.sample(mset, k)
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G.add_edges_from(zip([v] * len(targets), targets))
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return nx.projected_graph(G, range(n))
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@py_random_state(3)
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@nx._dispatchable(graphs=None, returns_graph=True)
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def general_random_intersection_graph(n, m, p, seed=None):
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"""Returns a random intersection graph with independent probabilities
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for connections between node and attribute sets.
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Parameters
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----------
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n : int
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The number of nodes in the first bipartite set (nodes)
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m : int
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The number of nodes in the second bipartite set (attributes)
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p : list of floats of length m
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Probabilities for connecting nodes to each attribute
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seed : integer, random_state, or None (default)
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Indicator of random number generation state.
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See :ref:`Randomness<randomness>`.
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See Also
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--------
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gnp_random_graph, uniform_random_intersection_graph
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References
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----------
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.. [1] Nikoletseas, S. E., Raptopoulos, C., and Spirakis, P. G.
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The existence and efficient construction of large independent sets
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in general random intersection graphs. In ICALP (2004), J. D´ıaz,
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J. Karhum¨aki, A. Lepist¨o, and D. Sannella, Eds., vol. 3142
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of Lecture Notes in Computer Science, Springer, pp. 1029–1040.
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"""
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if len(p) != m:
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raise ValueError("Probability list p must have m elements.")
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G = nx.empty_graph(n + m)
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mset = range(n, n + m)
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for u in range(n):
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for v, q in zip(mset, p):
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if seed.random() < q:
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G.add_edge(u, v)
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return nx.projected_graph(G, range(n))
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