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Source code for networkx.algorithms.bipartite.generators

# -*- coding: utf-8 -*-
#    Copyright (C) 2006-2011 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
#
# Authors: Aric Hagberg <aric.hagberg@gmail.com>
#                        Pieter Swart <swart@lanl.gov>
#                        Dan Schult <dschult@colgate.edu>
"""
Generators and functions for bipartite graphs.
"""
import math
import numbers
import random
from functools import reduce
import networkx as nx
from networkx.utils import nodes_or_number, py_random_state

__all__ = ['configuration_model',
           'havel_hakimi_graph',
           'reverse_havel_hakimi_graph',
           'alternating_havel_hakimi_graph',
           'preferential_attachment_graph',
           'random_graph',
           'gnmk_random_graph',
           'complete_bipartite_graph',
           ]


[docs]@nodes_or_number([0, 1]) def complete_bipartite_graph(n1, n2, create_using=None): """Returns the complete bipartite graph `K_{n_1,n_2}`. Composed of two partitions with `n_1` nodes in the first and `n_2` nodes in the second. Each node in the first is connected to each node in the second. Parameters ---------- n1 : integer Number of nodes for node set A. n2 : integer Number of nodes for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- Node labels are the integers 0 to `n_1 + n_2 - 1`. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. """ G = nx.empty_graph(0, create_using) if G.is_directed(): raise nx.NetworkXError("Directed Graph not supported") n1, top = n1 n2, bottom = n2 if isinstance(n2, numbers.Integral): bottom = [n1 + i for i in bottom] G.add_nodes_from(top, bipartite=0) G.add_nodes_from(bottom, bipartite=1) G.add_edges_from((u, v) for u in top for v in bottom) G.graph['name'] = "complete_bipartite_graph(%s,%s)" % (n1, n2) return G
[docs]@py_random_state(3) def configuration_model(aseq, bseq, create_using=None, seed=None): """Returns a random bipartite graph from two given degree sequences. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness<randomness>`. Nodes from the set A are connected to nodes in the set B by choosing randomly from the possible free stubs, one in A and one in B. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it you have to explicitly import the bipartite package. """ G = nx.empty_graph(0, create_using, default=nx.MultiGraph) if G.is_directed(): raise nx.NetworkXError("Directed Graph not supported") # length and sum of each sequence lena = len(aseq) lenb = len(bseq) suma = sum(aseq) sumb = sum(bseq) if not suma == sumb: raise nx.NetworkXError( 'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s' % (suma, sumb)) G = _add_nodes_with_bipartite_label(G, lena, lenb) if len(aseq) == 0 or max(aseq) == 0: return G # done if no edges # build lists of degree-repeated vertex numbers stubs = [] stubs.extend([[v] * aseq[v] for v in range(0, lena)]) astubs = [] astubs = [x for subseq in stubs for x in subseq] stubs = [] stubs.extend([[v] * bseq[v - lena] for v in range(lena, lena + lenb)]) bstubs = [] bstubs = [x for subseq in stubs for x in subseq] # shuffle lists seed.shuffle(astubs) seed.shuffle(bstubs) G.add_edges_from([[astubs[i], bstubs[i]] for i in range(suma)]) G.name = "bipartite_configuration_model" return G
[docs]def havel_hakimi_graph(aseq, bseq, create_using=None): """Returns a bipartite graph from two given degree sequences using a Havel-Hakimi style construction. Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to the highest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- This function is not imported in the main namespace. To use it you have to explicitly import the bipartite package. The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. """ G = nx.empty_graph(0, create_using, default=nx.MultiGraph) if G.is_directed(): raise nx.NetworkXError("Directed Graph not supported") # length of the each sequence naseq = len(aseq) nbseq = len(bseq) suma = sum(aseq) sumb = sum(bseq) if not suma == sumb: raise nx.NetworkXError( 'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s' % (suma, sumb)) G = _add_nodes_with_bipartite_label(G, naseq, nbseq) if len(aseq) == 0 or max(aseq) == 0: return G # done if no edges # build list of degree-repeated vertex numbers astubs = [[aseq[v], v] for v in range(0, naseq)] bstubs = [[bseq[v - naseq], v] for v in range(naseq, naseq + nbseq)] astubs.sort() while astubs: (degree, u) = astubs.pop() # take of largest degree node in the a set if degree == 0: break # done, all are zero # connect the source to largest degree nodes in the b set bstubs.sort() for target in bstubs[-degree:]: v = target[1] G.add_edge(u, v) target[0] -= 1 # note this updates bstubs too. if target[0] == 0: bstubs.remove(target) G.name = "bipartite_havel_hakimi_graph" return G
[docs]def reverse_havel_hakimi_graph(aseq, bseq, create_using=None): """Returns a bipartite graph from two given degree sequences using a Havel-Hakimi style construction. Nodes from set A are connected to nodes in the set B by connecting the highest degree nodes in set A to the lowest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- This function is not imported in the main namespace. To use it you have to explicitly import the bipartite package. The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. """ G = nx.empty_graph(0, create_using, default=nx.MultiGraph) if G.is_directed(): raise nx.NetworkXError("Directed Graph not supported") # length of the each sequence lena = len(aseq) lenb = len(bseq) suma = sum(aseq) sumb = sum(bseq) if not suma == sumb: raise nx.NetworkXError( 'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s' % (suma, sumb)) G = _add_nodes_with_bipartite_label(G, lena, lenb) if len(aseq) == 0 or max(aseq) == 0: return G # done if no edges # build list of degree-repeated vertex numbers astubs = [[aseq[v], v] for v in range(0, lena)] bstubs = [[bseq[v - lena], v] for v in range(lena, lena + lenb)] astubs.sort() bstubs.sort() while astubs: (degree, u) = astubs.pop() # take of largest degree node in the a set if degree == 0: break # done, all are zero # connect the source to the smallest degree nodes in the b set for target in bstubs[0:degree]: v = target[1] G.add_edge(u, v) target[0] -= 1 # note this updates bstubs too. if target[0] == 0: bstubs.remove(target) G.name = "bipartite_reverse_havel_hakimi_graph" return G
[docs]def alternating_havel_hakimi_graph(aseq, bseq, create_using=None): """Returns a bipartite graph from two given degree sequences using an alternating Havel-Hakimi style construction. Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to alternatively the highest and the lowest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- This function is not imported in the main namespace. To use it you have to explicitly import the bipartite package. The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. """ G = nx.empty_graph(0, create_using, default=nx.MultiGraph) if G.is_directed(): raise nx.NetworkXError("Directed Graph not supported") # length of the each sequence naseq = len(aseq) nbseq = len(bseq) suma = sum(aseq) sumb = sum(bseq) if not suma == sumb: raise nx.NetworkXError( 'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s' % (suma, sumb)) G = _add_nodes_with_bipartite_label(G, naseq, nbseq) if len(aseq) == 0 or max(aseq) == 0: return G # done if no edges # build list of degree-repeated vertex numbers astubs = [[aseq[v], v] for v in range(0, naseq)] bstubs = [[bseq[v - naseq], v] for v in range(naseq, naseq + nbseq)] while astubs: astubs.sort() (degree, u) = astubs.pop() # take of largest degree node in the a set if degree == 0: break # done, all are zero bstubs.sort() small = bstubs[0:degree // 2] # add these low degree targets large = bstubs[(-degree + degree // 2):] # and these high degree targets stubs = [x for z in zip(large, small) for x in z] # combine, sorry if len(stubs) < len(small) + len(large): # check for zip truncation stubs.append(large.pop()) for target in stubs: v = target[1] G.add_edge(u, v) target[0] -= 1 # note this updates bstubs too. if target[0] == 0: bstubs.remove(target) G.name = "bipartite_alternating_havel_hakimi_graph" return G
[docs]@py_random_state(3) def preferential_attachment_graph(aseq, p, create_using=None, seed=None): """Create a bipartite graph with a preferential attachment model from a given single degree sequence. Parameters ---------- aseq : list Degree sequence for node set A. p : float Probability that a new bottom node is added. create_using : NetworkX graph instance, optional Return graph of this type. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness<randomness>`. References ---------- .. [1] Guillaume, J.L. and Latapy, M., Bipartite graphs as models of complex networks. Physica A: Statistical Mechanics and its Applications, 2006, 371(2), pp.795-813. .. [2] Jean-Loup Guillaume and Matthieu Latapy, Bipartite structure of all complex networks, Inf. Process. Lett. 90, 2004, pg. 215-221 https://doi.org/10.1016/j.ipl.2004.03.007 Notes ----- This function is not imported in the main namespace. To use it you have to explicitly import the bipartite package. """ G = nx.empty_graph(0, create_using, default=nx.MultiGraph) if G.is_directed(): raise nx.NetworkXError("Directed Graph not supported") if p > 1: raise nx.NetworkXError("probability %s > 1" % (p)) naseq = len(aseq) G = _add_nodes_with_bipartite_label(G, naseq, 0) vv = [[v] * aseq[v] for v in range(0, naseq)] while vv: while vv[0]: source = vv[0][0] vv[0].remove(source) if seed.random() < p or G.number_of_nodes() == naseq: target = G.number_of_nodes() G.add_node(target, bipartite=1) G.add_edge(source, target) else: bb = [[b] * G.degree(b) for b in range(naseq, G.number_of_nodes())] # flatten the list of lists into a list. bbstubs = reduce(lambda x, y: x + y, bb) # choose preferentially a bottom node. target = seed.choice(bbstubs) G.add_node(target, bipartite=1) G.add_edge(source, target) vv.remove(vv[0]) G.name = "bipartite_preferential_attachment_model" return G
[docs]@py_random_state(3) def random_graph(n, m, p, seed=None, directed=False): """Returns a bipartite random graph. This is a bipartite version of the binomial (Erdős-Rényi) graph. Parameters ---------- n : int The number of nodes in the first bipartite set. m : int The number of nodes in the second bipartite set. p : float Probability for edge creation. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness<randomness>`. directed : bool, optional (default=False) If True return a directed graph Notes ----- This function is not imported in the main namespace. To use it you have to explicitly import the bipartite package. The bipartite random graph algorithm chooses each of the n*m (undirected) or 2*nm (directed) possible edges with probability p. This algorithm is $O(n+m)$ where $m$ is the expected number of edges. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. See Also -------- gnp_random_graph, configuration_model References ---------- .. [1] Vladimir Batagelj and Ulrik Brandes, "Efficient generation of large random networks", Phys. Rev. E, 71, 036113, 2005. """ G = nx.Graph() G = _add_nodes_with_bipartite_label(G, n, m) if directed: G = nx.DiGraph(G) G.name = "fast_gnp_random_graph(%s,%s,%s)" % (n, m, p) if p <= 0: return G if p >= 1: return nx.complete_bipartite_graph(n, m) lp = math.log(1.0 - p) v = 0 w = -1 while v < n: lr = math.log(1.0 - seed.random()) w = w + 1 + int(lr / lp) while w >= m and v < n: w = w - m v = v + 1 if v < n: G.add_edge(v, n + w) if directed: # use the same algorithm to # add edges from the "m" to "n" set v = 0 w = -1 while v < n: lr = math.log(1.0 - seed.random()) w = w + 1 + int(lr / lp) while w >= m and v < n: w = w - m v = v + 1 if v < n: G.add_edge(n + w, v) return G
[docs]@py_random_state(3) def gnmk_random_graph(n, m, k, seed=None, directed=False): """Returns a random bipartite graph G_{n,m,k}. Produces a bipartite graph chosen randomly out of the set of all graphs with n top nodes, m bottom nodes, and k edges. Parameters ---------- n : int The number of nodes in the first bipartite set. m : int The number of nodes in the second bipartite set. k : int The number of edges seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness<randomness>`. directed : bool, optional (default=False) If True return a directed graph Examples -------- from nx.algorithms import bipartite G = bipartite.gnmk_random_graph(10,20,50) See Also -------- gnm_random_graph Notes ----- This function is not imported in the main namespace. To use it you have to explicitly import the bipartite package. If k > m * n then a complete bipartite graph is returned. This graph is a bipartite version of the `G_{nm}` random graph model. """ G = nx.Graph() G = _add_nodes_with_bipartite_label(G, n, m) if directed: G = nx.DiGraph(G) G.name = "bipartite_gnm_random_graph(%s,%s,%s)" % (n, m, k) if n == 1 or m == 1: return G max_edges = n * m # max_edges for bipartite networks if k >= max_edges: # Maybe we should raise an exception here return nx.complete_bipartite_graph(n, m, create_using=G) top = [n for n, d in G.nodes(data=True) if d['bipartite'] == 0] bottom = list(set(G) - set(top)) edge_count = 0 while edge_count < k: # generate random edge,u,v u = seed.choice(top) v = seed.choice(bottom) if v in G[u]: continue else: G.add_edge(u, v) edge_count += 1 return G
def _add_nodes_with_bipartite_label(G, lena, lenb): G.add_nodes_from(range(0, lena + lenb)) b = dict(zip(range(0, lena), [0] * lena)) b.update(dict(zip(range(lena, lena + lenb), [1] * lenb))) nx.set_node_attributes(G, b, 'bipartite') return G