ó ú£Õ\c@s¼dZddlZddlmZdjdddgƒZdd d d gZd „Zd „Z d„Z d„Z d„Z d„Z d„Zd„Zd„Zd„Zd„Zd„ZdS(s Graph products. iÿÿÿÿN(tproducts sAric Hagberg (hagberg@lanl.gov)sPieter Swart (swart@lanl.gov)s?Dan Schult(dschult@colgate.edu)Ben Edwards(bedwards@cs.unm.edu)ttensor_producttcartesian_producttlexicographic_producttstrong_productcs-t‡‡fd†tˆƒtˆƒBDƒƒS(Nc3s3|])}|ˆj|ƒˆj|ƒffVqdS(N(tget(t.0tk(td1td2(s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pys s(tdicttset(RR ((RR s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt _dict_productsccsLxEt||ƒD]4\}}||ft|j||j|ƒfVqWdS(N(RR tnode(tGtHtutv((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt _node_productsc csc|jƒ rŒ|jƒ rŒxo|jdtƒD]X\}}}xF|jdtƒD]2\}}}||f||ft||ƒfVqOWq-Wn|jƒ r#|jƒr#x{|jdtƒD]d\}}}xR|jdtdtƒD]8\}}}}||f||f|t||ƒfVqàWq¸Wn|jƒrº|jƒ rºx{|jdtdtƒD]^\}}}}xI|jdtƒD]5\}}}||f||f|t||ƒfVqzWqUWn|jƒr_|jƒr_xŠ|jdtdtƒD]m\}}} }xX|jdtdtƒD]>\}}}}||f||f| |ft||ƒfVqWqëWndS(Ntdatatkeys(t is_multigrapht edges_itertTrueR ( RRRRtctxtytdRtj((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt_directed_edges_cross_edgess ""."+1+"1++c csc|jƒ rŒ|jƒ rŒxo|jdtƒD]X\}}}xF|jdtƒD]2\}}}||f||ft||ƒfVqOWq-Wn|jƒ r#|jƒr#x{|jdtƒD]d\}}}xR|jdtdtƒD]8\}}}}||f||f|t||ƒfVqàWq¸Wn|jƒrº|jƒ rºx{|jdtdtƒD]^\}}}}xI|jdtƒD]5\}}}||f||f|t||ƒfVqzWqUWn|jƒr_|jƒr_xŠ|jdtdtƒD]m\}}} }xX|jdtdtƒD]>\}}}}||f||f| |ft||ƒfVqWqëWndS(NRR(RRRR ( RRRRRRRRRR((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt_undirected_edges_cross_edges0s ""."+1+"1++ccsí|jƒrlxÚ|jdtdtƒD]@\}}}}x+|D]#}||f||f||fVq>Wq%Wn}xz|jdtƒD]f\}}}xT|D]L}|jƒrÇ||f||fd|fVq•||f||f|fVq•WqWdS(NRR(RRRtNone(RRRRRRR((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt_edges_cross_nodesBs + ("   ccsí|jƒrlxÚ|D]R}xI|jdtdtƒD]/\}}}}||f||f||fVq2WqWn}xz|D]r}xi|jdtƒD]U\}}}|jƒrÇ||f||fd|fVqŒ||f||f|fVqŒWqsWdS(NRR(RRRR(RRRRRRR((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt_nodes_cross_edgesPs  +( "  ccs|jƒr}xü|jdtdtƒD]Q\}}}}x<|D]4}x+|D]#}||f||f||fVqKWq>Wq%WnŽx‹|jdtƒD]w\}}}xe|D]]}xT|D]L}|jƒrå||f||fd|fVq³||f||f|fVq³Wq¦WqWdS(NRR(RRRR(RRRRRRRR((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt_edges_cross_nodes_and_nodes]s +  ,"    cCs|jƒ|jƒks-tjddƒ‚n|jƒsE|jƒrTtjƒ}n tjƒ}|jƒr{|jƒ}n|S(Ns G and H must be both directed orsboth undirected(t is_directedtnxt NetworkXErrorRt MultiGraphtGrapht to_directed(RRtGH((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyt_init_product_graphls    cCsƒt||ƒ}|jt||ƒƒ|jt||ƒƒ|jƒs`|jt||ƒƒnd|jd|jd|_|S(sÍReturn 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(data=True) [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph sTensor product(t,t)(R*tadd_nodes_fromRtadd_edges_fromRR#Rtname(RRR)((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyRys- cCs¡|jƒ|jƒks-tjddƒ‚nt||ƒ}|jt||ƒƒ|jt||ƒƒ|jt||ƒƒd|j d|j d|_ |S(sÏReturn 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, $V(P)=V(G) imes V(H)$. 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.tensor_product(G,H) >>> P.nodes(data=True) [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph s G and H must be both directed orsboth undirectedsCartesian product(R+R,( R#R$R%R*R-RR.R R!R/(RRR)((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyR®s+  cCstt||ƒ}|jt||ƒƒ|jt||ƒƒ|jt||ƒƒd|jd|jd|_|S(s¯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, $V(P)=V(G) imes V(H)$. 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.tensor_product(G,H) >>> P.nodes(data=True) [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph sLexographic product(R+R,(R*R-RR.R"R!R/(RRR)((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyRãs *cCs¯t||ƒ}|jt||ƒƒ|jt||ƒƒ|jt||ƒƒ|jt||ƒƒ|jƒsŒ|jt||ƒƒnd|j d|j d|_ |S(såReturn 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, $V(P)=V(G) imes V(H)$. 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.tensor_product(G,H) >>> P.nodes(data=True) [((0, 'a'), {'a1': (True, None), 'a2': (None, 'Spam')})] Edge attributes and edge keys (for multigraphs) are also copied to the new product graph sStrong product(R+R,( R*R-RR.R!R RR#RR/(RRR)((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyRs, (t__doc__tnetworkxR$t itertoolsRtjoint __author__t__all__R RRRR R!R"R*RRRR(((s]/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/operators/product.pyts&           5 5 3