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"""
Generators for random intersection graphs.
"""
import networkx as nx
from networkx.utils import py_random_state
__all__ = [
"uniform_random_intersection_graph",
"k_random_intersection_graph",
"general_random_intersection_graph",
]
@py_random_state(3)
@nx._dispatch(graphs=None)
def uniform_random_intersection_graph(n, m, p, seed=None):
"""Returns 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 : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
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.
"""
from networkx.algorithms import bipartite
G = bipartite.random_graph(n, m, p, seed)
return nx.projected_graph(G, range(n))
@py_random_state(3)
@nx._dispatch(graphs=None)
def k_random_intersection_graph(n, m, k, seed=None):
"""Returns 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 : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
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 = seed.sample(mset, k)
G.add_edges_from(zip([v] * len(targets), targets))
return nx.projected_graph(G, range(n))
@py_random_state(3)
@nx._dispatch(graphs=None)
def general_random_intersection_graph(n, m, p, seed=None):
"""Returns 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 : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
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 seed.random() < q:
G.add_edge(u, v)
return nx.projected_graph(G, range(n))
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