121 lines
3.8 KiB
Python
121 lines
3.8 KiB
Python
|
"""
|
|||
|
|
Generators for random intersection graphs.
|
|||
|
|
"""
|
|||
|
|
import networkx as nx
|
|||
|
|
from networkx.algorithms import bipartite
|
|||
|
|
from networkx.utils import py_random_state
|
|||
|
|
|
|||
|
|
__all__ = [
|
|||
|
|
"uniform_random_intersection_graph",
|
|||
|
|
"k_random_intersection_graph",
|
|||
|
|
"general_random_intersection_graph",
|
|||
|
|
]
|
|||
|
|
|
|||
|
|
|
|||
|
|
@py_random_state(3)
|
|||
|
|
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.
|
|||
|
|
"""
|
|||
|
|
G = bipartite.random_graph(n, m, p, seed)
|
|||
|
|
return nx.projected_graph(G, range(n))
|
|||
|
|
|
|||
|
|
|
|||
|
|
@py_random_state(3)
|
|||
|
|
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)
|
|||
|
|
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))
|