| # -*- 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', |
| ] |
| |
| 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)) |
| |
| 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)) |
| |
| 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)) |
| |