# Source code for networkx.algorithms.bipartite.generators

"""
Generators and functions for bipartite graphs.
"""
import math
import numbers
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}`. The graph is composed of two partitions with nodes 0 to (n1 - 1) in the first and nodes n1 to (n1 + n2 - 1) in the second. Each node in the first is connected to each node in the second. Parameters ---------- n1, n2 : integer or iterable container of nodes If integers, nodes are from `range(n1)` and `range(n1, n1 + n2)`. If a container, the elements are the nodes. create_using : NetworkX graph instance, (default: nx.Graph) Return graph of this type. Notes ----- Nodes are the integers 0 to `n1 + n2 - 1` unless either n1 or n2 are containers of nodes. If only one of n1 or n2 are integers, that integer is replaced by `range` of that integer. 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 use nx.bipartite.complete_bipartite_graph """ 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(n1, numbers.Integral) and 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) if len(G) != len(top) + len(bottom): raise nx.NetworkXError("Inputs n1 and n2 must contain distinct nodes") G.add_edges_from((u, v) for u in top for v in bottom) G.graph["name"] = f"complete_bipartite_graph({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>`. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from set A are connected to nodes in 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 use nx.bipartite.configuration_model """ 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( f"invalid degree sequences, sum(aseq)!=sum(bseq),{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 = [[v] * aseq[v] for v in range(0, lena)] astubs = [x for subseq in stubs for x in subseq] stubs = [[v] * bseq[v - lena] for v in range(lena, lena + lenb)] 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. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). 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 ----- 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 use nx.bipartite.havel_hakimi_graph """ 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( f"invalid degree sequences, sum(aseq)!=sum(bseq),{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. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). 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 ----- 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 use nx.bipartite.reverse_havel_hakimi_graph """ 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( f"invalid degree sequences, sum(aseq)!=sum(bseq),{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. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). 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 ----- 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 use nx.bipartite.alternating_havel_hakimi_graph """ 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( f"invalid degree sequences, sum(aseq)!=sum(bseq),{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) :] # now 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. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes starting with node len(aseq). The number of nodes in set B is random. 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 ----- 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 use nx.bipartite.preferential_attachment_graph """ 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(f"probability {p} > 1") 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 len(G) == naseq: target = len(G) G.add_node(target, bipartite=1) G.add_edge(source, target) else: bb = [[b] * G.degree(b) for b in range(naseq, len(G))] # 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. The graph is composed of two partitions. Set A has nodes 0 to (n - 1) and set B has nodes n to (n + m - 1). 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 ----- 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. This function is not imported in the main namespace. To use it use nx.bipartite.random_graph 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 = f"fast_gnp_random_graph({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. The graph is composed of two sets of nodes. Set A has nodes 0 to (n - 1) and set B has nodes n to (n + m - 1). 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 ----- If k > m * n then a complete bipartite graph is returned. This graph is a bipartite version of the `G_{nm}` random graph model. 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 use nx.bipartite.gnmk_random_graph """ G = nx.Graph() G = _add_nodes_with_bipartite_label(G, n, m) if directed: G = nx.DiGraph(G) G.name = f"bipartite_gnm_random_graph({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