Source code for networkx.generators.intersection

# -*- coding: utf-8 -*-
"""
Generators for random intersection graphs.
"""
#    Copyright (C) 2011 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
import random
import networkx as nx
__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)'])

__all__ = ['uniform_random_intersection_graph',
           'k_random_intersection_graph',
           'general_random_intersection_graph',
           ]

[docs]def uniform_random_intersection_graph(n, m, p, seed=None):
    """Return a uniform random intersection graph.

    Parameters
    ----------
    n : int
        The number of nodes in the first bipartite set (nodes)
    m : int
        The number of nodes in the second bipartite set (attributes)
    p : float
        Probability of connecting nodes between bipartite sets  
    seed : int, optional
        Seed for random number generator (default=None). 

    See Also
    --------
    gnp_random_graph

    References
    ----------
    .. [1] K.B. Singer-Cohen, Random Intersection Graphs, 1995,
       PhD thesis, Johns Hopkins University
    .. [2] Fill, J. A., Scheinerman, E. R., and Singer-Cohen, K. B., 
       Random intersection graphs when m = !(n): 
       An equivalence theorem relating the evolution of the g(n, m, p)
       and g(n, p) models. Random Struct. Algorithms 16, 2 (2000), 156–176.
    """
    G=nx.bipartite_random_graph(n, m, p, seed=seed)
    return nx.projected_graph(G, range(n)) 

[docs]def k_random_intersection_graph(n,m,k):
    """Return a intersection graph with randomly chosen attribute sets for
    each node that are of equal size (k). 

    Parameters
    ----------
    n : int
        The number of nodes in the first bipartite set (nodes)
    m : int
        The number of nodes in the second bipartite set (attributes)
    k : float
        Size of attribute set to assign to each node.
    seed : int, optional
        Seed for random number generator (default=None). 

    See Also
    --------
    gnp_random_graph, uniform_random_intersection_graph

    References
    ----------
    .. [1] Godehardt, E., and Jaworski, J.
       Two models of random intersection graphs and their applications.
       Electronic Notes in Discrete Mathematics 10 (2001), 129--132.
    """
    G = nx.empty_graph(n + m)
    mset = range(n,n+m)
    for v in range(n):
        targets = random.sample(mset, k)
        G.add_edges_from(zip([v]*len(targets), targets))
    return nx.projected_graph(G, range(n))

[docs]def general_random_intersection_graph(n,m,p):
    """Return a random intersection graph with independent probabilities
    for connections between node and attribute sets.

    Parameters
    ----------
    n : int
        The number of nodes in the first bipartite set (nodes)
    m : int
        The number of nodes in the second bipartite set (attributes)
    p : list of floats of length m
        Probabilities for connecting nodes to each attribute
    seed : int, optional
        Seed for random number generator (default=None). 
    
    See Also
    --------
    gnp_random_graph, uniform_random_intersection_graph

    References
    ----------
    .. [1] Nikoletseas, S. E., Raptopoulos, C., and Spirakis, P. G. 
       The existence and efficient construction of large independent sets 
       in general random intersection graphs. In ICALP (2004), J. D´ıaz, 
       J. Karhum¨aki, A. Lepist¨o, and D. Sannella, Eds., vol. 3142
       of Lecture Notes in Computer Science, Springer, pp. 1029–1040.
    """
    if len(p)!=m:
        raise ValueError("Probability list p must have m elements.")
    G = nx.empty_graph(n + m)
    mset = range(n,n+m)
    for u in range(n):
        for v,q in zip(mset,p):
            if random.random()<q:
                G.add_edge(u,v)
    return nx.projected_graph(G, range(n))