Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.operators.product

"""
Graph products.
"""
#    Copyright (C) 2011 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
import networkx as nx
from itertools import product

__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Dan Schult(dschult@colgate.edu)'
'Ben Edwards(bedwards@cs.unm.edu)'])

__all__ = ['tensor_product','cartesian_product',
'lexicographic_product', 'strong_product']

def _dict_product(d1,d2):
return dict((k,(d1.get(k),d2.get(k))) for k in set(d1)|set(d2))

# Generators for producting graph products
def _node_product(G,H):
for u,v in product(G, H):
yield ((u,v), _dict_product(G.node[u], H.node[v]))

def _directed_edges_cross_edges(G,H):
if not G.is_multigraph() and not H.is_multigraph():
for u,v,c in G.edges_iter(data=True):
for x,y,d in H.edges_iter(data=True):
yield (u,x),(v,y),_dict_product(c,d)
if not G.is_multigraph() and H.is_multigraph():
for u,v,c in G.edges_iter(data=True):
for x,y,k,d in H.edges_iter(data=True,keys=True):
yield (u,x),(v,y),k,_dict_product(c,d)
if G.is_multigraph() and not H.is_multigraph():
for u,v,k,c in G.edges_iter(data=True,keys=True):
for x,y,d in H.edges_iter(data=True):
yield (u,x),(v,y),k,_dict_product(c,d)
if G.is_multigraph() and H.is_multigraph():
for u,v,j,c in G.edges_iter(data=True,keys=True):
for x,y,k,d in H.edges_iter(data=True,keys=True):
yield (u,x),(v,y),(j,k),_dict_product(c,d)

def _undirected_edges_cross_edges(G,H):
if not G.is_multigraph() and not H.is_multigraph():
for u,v,c in G.edges_iter(data=True):
for x,y,d in H.edges_iter(data=True):
yield (v,x),(u,y),_dict_product(c,d)
if not G.is_multigraph() and H.is_multigraph():
for u,v,c in G.edges_iter(data=True):
for x,y,k,d in H.edges_iter(data=True,keys=True):
yield (v,x),(u,y),k,_dict_product(c,d)
if G.is_multigraph() and not H.is_multigraph():
for u,v,k,c in G.edges_iter(data=True,keys=True):
for x,y,d in H.edges_iter(data=True):
yield (v,x),(u,y),k,_dict_product(c,d)
if G.is_multigraph() and H.is_multigraph():
for u,v,j,c in G.edges_iter(data=True,keys=True):
for x,y,k,d in H.edges_iter(data=True,keys=True):
yield (v,x),(u,y),(j,k),_dict_product(c,d)

def _edges_cross_nodes(G,H):
if G.is_multigraph():
for u,v,k,d in G.edges_iter(data=True,keys=True):
for x in H:
yield (u,x),(v,x),k,d
else:
for u,v,d in G.edges_iter(data=True):
for x in H:
if H.is_multigraph():
yield (u,x),(v,x),None,d
else:
yield (u,x),(v,x),d

def _nodes_cross_edges(G,H):
if H.is_multigraph():
for x in G:
for u,v,k,d in H.edges_iter(data=True,keys=True):
yield (x,u),(x,v),k,d
else:
for x in G:
for u,v,d in H.edges_iter(data=True):
if G.is_multigraph():
yield (x,u),(x,v),None,d
else:
yield (x,u),(x,v),d

def _edges_cross_nodes_and_nodes(G,H):
if G.is_multigraph():
for u,v,k,d in G.edges_iter(data=True,keys=True):
for x in H:
for y in H:
yield (u,x),(v,y),k,d
else:
for u,v,d in G.edges_iter(data=True):
for x in H:
for y in H:
if H.is_multigraph():
yield (u,x),(v,y),None,d
else:
yield (u,x),(v,y),d

def _init_product_graph(G,H):
if not G.is_directed() == H.is_directed():
raise nx.NetworkXError("G and H must be both directed or",
"both undirected")
if G.is_multigraph() or H.is_multigraph():
GH = nx.MultiGraph()
else:
GH = nx.Graph()
if G.is_directed():
GH = GH.to_directed()
return GH

[docs]def tensor_product(G,H): r"""Return the tensor product of G and H. The tensor product P of the graphs G and H has a node set that is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$. P has an edge ((u,v),(x,y)) if and only if (u,v) is an edge in G and (x,y) is an edge in H. Sometimes referred to as the categorical product. Parameters ---------- G, H: graphs Networkx graphs. Returns ------- P: NetworkX graph The tensor product of G and H. P will be a multi-graph if either G or H is a multi-graph. Will be a directed if G and H are directed, and undirected if G and H are undirected. Raises ------ NetworkXError If G and H are not both directed or both undirected. Notes ----- Node attributes in P are two-tuple of the G and H node attributes. Missing attributes are assigned None. For example >>> G = nx.Graph() >>> H = nx.Graph() >>> G.add_node(0,a1=True) >>> H.add_node('a',a2='Spam') >>> P = nx.tensor_product(G,H) >>> P.nodes() [(0, 'a')] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph """ GH = _init_product_graph(G,H) GH.add_nodes_from(_node_product(G,H)) GH.add_edges_from(_directed_edges_cross_edges(G,H)) if not GH.is_directed(): GH.add_edges_from(_undirected_edges_cross_edges(G,H)) GH.name = "Tensor product("+G.name+","+H.name+")" return GH
[docs]def cartesian_product(G,H): """Return the Cartesian product of G and H. The tensor product P of the graphs G and H has a node set that is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$. P has an edge ((u,v),(x,y)) if and only if (u,v) is an edge in G and x==y or and (x,y) is an edge in H and u==v. and (x,y) is an edge in H. Parameters ---------- G, H: graphs Networkx graphs. Returns ------- P: NetworkX graph The Cartesian product of G and H. P will be a multi-graph if either G or H is a multi-graph. Will be a directed if G and H are directed, and undirected if G and H are undirected. Raises ------ NetworkXError If G and H are not both directed or both undirected. Notes ----- Node attributes in P are two-tuple of the G and H node attributes. Missing attributes are assigned None. For example >>> G = nx.Graph() >>> H = nx.Graph() >>> G.add_node(0,a1=True) >>> H.add_node('a',a2='Spam') >>> P = nx.cartesian_product(G,H) >>> P.nodes() [(0, 'a')] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph """ if not G.is_directed() == H.is_directed(): raise nx.NetworkXError("G and H must be both directed or", "both undirected") GH = _init_product_graph(G,H) GH.add_nodes_from(_node_product(G,H)) GH.add_edges_from(_edges_cross_nodes(G,H)) GH.add_edges_from(_nodes_cross_edges(G,H)) GH.name = "Cartesian product("+G.name+","+H.name+")" return GH
[docs]def lexicographic_product(G,H): """Return the lexicographic product of G and H. The lexicographical product P of the graphs G and H has a node set that is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$. P has an edge ((u,v),(x,y)) if and only if (u,v) is an edge in G or u==v and (x,y) is an edge in H. Parameters ---------- G, H: graphs Networkx graphs. Returns ------- P: NetworkX graph The Cartesian product of G and H. P will be a multi-graph if either G or H is a multi-graph. Will be a directed if G and H are directed, and undirected if G and H are undirected. Raises ------ NetworkXError If G and H are not both directed or both undirected. Notes ----- Node attributes in P are two-tuple of the G and H node attributes. Missing attributes are assigned None. For example >>> G = nx.Graph() >>> H = nx.Graph() >>> G.add_node(0,a1=True) >>> H.add_node('a',a2='Spam') >>> P = nx.lexicographic_product(G,H) >>> P.nodes() [(0, 'a')] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph """ GH = _init_product_graph(G,H) GH.add_nodes_from(_node_product(G,H)) # Edges in G regardless of H designation GH.add_edges_from(_edges_cross_nodes_and_nodes(G,H)) # For each x in G, only if there is an edge in H GH.add_edges_from(_nodes_cross_edges(G,H)) GH.name = "Lexicographic product("+G.name+","+H.name+")" return GH
[docs]def strong_product(G,H): """Return the strong product of G and H. The strong product P of the graphs G and H has a node set that is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$. P has an edge ((u,v),(x,y)) if and only if u==v and (x,y) is an edge in H, or x==y and (u,v) is an edge in G, or (u,v) is an edge in G and (x,y) is an edge in H. Parameters ---------- G, H: graphs Networkx graphs. Returns ------- P: NetworkX graph The Cartesian product of G and H. P will be a multi-graph if either G or H is a multi-graph. Will be a directed if G and H are directed, and undirected if G and H are undirected. Raises ------ NetworkXError If G and H are not both directed or both undirected. Notes ----- Node attributes in P are two-tuple of the G and H node attributes. Missing attributes are assigned None. For example >>> G = nx.Graph() >>> H = nx.Graph() >>> G.add_node(0,a1=True) >>> H.add_node('a',a2='Spam') >>> P = nx.strong_product(G,H) >>> P.nodes() [(0, 'a')] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph """ GH = _init_product_graph(G,H) GH.add_nodes_from(_node_product(G,H)) GH.add_edges_from(_nodes_cross_edges(G,H)) GH.add_edges_from(_edges_cross_nodes(G,H)) GH.add_edges_from(_directed_edges_cross_edges(G,H)) if not GH.is_directed(): GH.add_edges_from(_undirected_edges_cross_edges(G,H)) GH.name = "Strong product("+G.name+","+H.name+")" return GH