ó ú£Õ\c@sˆdZddlZdjddgƒZdddd d d gZed „Zed „Zd„Z e d„Z dd„Z dd„ZdS(s7One-mode (unipartite) projections of bipartite graphs. iÿÿÿÿNs s%Aric Hagberg s%Jordi Torrents tprojecttprojected_graphtweighted_projected_grapht&collaboration_weighted_projected_grapht overlap_weighted_projected_grapht generic_weighted_projected_graphc s«ˆjƒrtjdƒ‚nˆjƒrTt}|rEtjƒ}q{tjƒ}n't}|rotjƒ}n tj ƒ}|j j ˆj ƒ|j ‡fd†|Dƒƒxù|D]ñ‰t ‡fd†ˆˆDƒƒt ˆgƒ}|r†xµ|D]}|r"t ˆˆƒt ˆj|ƒ@}nt ˆˆƒt ˆ|ƒ@}x<|D]4}|jˆ||ƒsG|jˆ|d|ƒqGqGWqòWq²|j‡fd†|Dƒƒq²W|S(s‰Returns the projection of B onto one of its node sets. Returns the graph G that is the projection of the bipartite graph B onto the specified nodes. They retain their attributes and are connected in G if they have a common neighbor in B. Parameters ---------- B : NetworkX graph The input graph should be bipartite. nodes : list or iterable Nodes to project onto (the "bottom" nodes). multigraph: bool (default=False) If True return a multigraph where the multiple edges represent multiple shared neighbors. They edge key in the multigraph is assigned to the label of the neighbor. Returns ------- Graph : NetworkX graph or multigraph A graph that is the projection onto the given nodes. Examples -------- >>> from networkx.algorithms import bipartite >>> B = nx.path_graph(4) >>> G = bipartite.projected_graph(B, [1,3]) >>> print(G.nodes()) [1, 3] >>> print(G.edges()) [(1, 3)] If nodes `a`, and `b` are connected through both nodes 1 and 2 then building a multigraph results in two edges in the projection onto [`a`,`b`]: >>> B = nx.Graph() >>> B.add_edges_from([('a', 1), ('b', 1), ('a', 2), ('b', 2)]) >>> G = bipartite.projected_graph(B, ['a', 'b'], multigraph=True) >>> print(G.edges(keys=True)) [('a', 'b', 1), ('a', 'b', 2)] Notes ------ No attempt is made to verify that the input graph B is bipartite. Returns a simple graph that is the projection of the bipartite graph B onto the set of nodes given in list nodes. If multigraph=True then a multigraph is returned with an edge for every shared neighbor. Directed graphs are allowed as input. The output will also then be a directed graph with edges if there is a directed path between the nodes. The graph and node properties are (shallow) copied to the projected graph. See Also -------- is_bipartite, is_bipartite_node_set, sets, weighted_projected_graph, collaboration_weighted_projected_graph, overlap_weighted_projected_graph, generic_weighted_projected_graph snot defined for multigraphsc3s"|]}|ˆj|fVqdS(N(tnode(t.0tn(tB(s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys gsc3s&|]}ˆ|D] }|VqqdS(N((Rtnbrtv(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys istkeyc3s|]}ˆ|fVqdS(N((RR(tu(s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys ts(t is_multigraphtnxt NetworkXErrort is_directedtTruet MultiDiGraphtDiGraphtFalset MultiGraphtGraphtgraphtupdatetadd_nodes_fromtsettpredthas_edgetadd_edgetadd_edges_from( R tnodest multigraphtdirectedtGtnbrs2Rtlinkstl((R R s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pyRs2D    - $ $!c sWˆjƒrtjdƒ‚nˆjƒrBˆj}tjƒ}nˆj}tjƒ}|jj ˆjƒ|j ‡fd†|Dƒƒt t ˆƒt |ƒƒ}x­|D]¥}t ˆ|ƒ}t ‡fd†|Dƒƒt |gƒ}xc|D][} t || ƒ} || @} |s%t | ƒ} nt | ƒ|} |j|| d| ƒqðWqªW|S(sãReturns a weighted projection of B onto one of its node sets. The weighted projected graph is the projection of the bipartite network B onto the specified nodes with weights representing the number of shared neighbors or the ratio between actual shared neighbors and possible shared neighbors if ratio=True [1]_. The nodes retain their attributes and are connected in the resulting graph if they have an edge to a common node in the original graph. Parameters ---------- B : NetworkX graph The input graph should be bipartite. nodes : list or iterable Nodes to project onto (the "bottom" nodes). ratio: Bool (default=False) If True, edge weight is the ratio between actual shared neighbors and possible shared neighbors. If False, edges weight is the number of shared neighbors. Returns ------- Graph : NetworkX graph A graph that is the projection onto the given nodes. Examples -------- >>> from networkx.algorithms import bipartite >>> B = nx.path_graph(4) >>> G = bipartite.weighted_projected_graph(B, [1,3]) >>> print(G.nodes()) [1, 3] >>> print(G.edges(data=True)) [(1, 3, {'weight': 1})] >>> G = bipartite.weighted_projected_graph(B, [1,3], ratio=True) >>> print(G.edges(data=True)) [(1, 3, {'weight': 0.5})] Notes ------ No attempt is made to verify that the input graph B is bipartite. The graph and node properties are (shallow) copied to the projected graph. See Also -------- is_bipartite, is_bipartite_node_set, sets, collaboration_weighted_projected_graph, overlap_weighted_projected_graph, generic_weighted_projected_graph projected_graph References ---------- .. [1] Borgatti, S.P. and Halgin, D. In press. "Analyzing Affiliation Networks". In Carrington, P. and Scott, J. (eds) The Sage Handbook of Social Network Analysis. Sage Publications. snot defined for multigraphsc3s"|]}|ˆj|fVqdS(N(R(RR(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys ¾sc3s&|]}ˆ|D] }|VqqdS(N((RR R(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys Âstweight(RRRRRRtadjRRRRtfloattlenRR( R R tratioRR#tn_topR tunbrsR$R tvnbrstcommonR'((R s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pyRws*>      )  c s]ˆjƒrtjdƒ‚nˆjƒrBˆj}tjƒ}nˆj}tjƒ}|jj ˆjƒ|j ‡fd†|DƒƒxÏ|D]Ç}t ˆ|ƒ}t ‡fd†|Dƒƒt |gƒ}x…|D]}}t ||ƒ}||@} t g| D]4} t ˆ| ƒdkrþdt ˆ| ƒd^qþƒ} |j||d| ƒqÔWqŽW|S(s7Newman's weighted projection of B onto one of its node sets. The collaboration weighted projection is the projection of the bipartite network B onto the specified nodes with weights assigned using Newman's collaboration model [1]_: .. math:: w_{v,u} = \sum_k \frac{\delta_{v}^{w} \delta_{w}^{k}}{k_w - 1} where `v` and `u` are nodes from the same bipartite node set, and `w` is a node of the opposite node set. The value `k_w` is the degree of node `w` in the bipartite network and `\delta_{v}^{w}` is 1 if node `v` is linked to node `w` in the original bipartite graph or 0 otherwise. The nodes retain their attributes and are connected in the resulting graph if have an edge to a common node in the original bipartite graph. Parameters ---------- B : NetworkX graph The input graph should be bipartite. nodes : list or iterable Nodes to project onto (the "bottom" nodes). Returns ------- Graph : NetworkX graph A graph that is the projection onto the given nodes. Examples -------- >>> from networkx.algorithms import bipartite >>> B = nx.path_graph(5) >>> B.add_edge(1,5) >>> G = bipartite.collaboration_weighted_projected_graph(B, [0, 2, 4, 5]) >>> print(G.nodes()) [0, 2, 4, 5] >>> for edge in G.edges(data=True): print(edge) ... (0, 2, {'weight': 0.5}) (0, 5, {'weight': 0.5}) (2, 4, {'weight': 1.0}) (2, 5, {'weight': 0.5}) Notes ------ No attempt is made to verify that the input graph B is bipartite. The graph and node properties are (shallow) copied to the projected graph. See Also -------- is_bipartite, is_bipartite_node_set, sets, weighted_projected_graph, overlap_weighted_projected_graph, generic_weighted_projected_graph, projected_graph References ---------- .. [1] Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality, M. E. J. Newman, Phys. Rev. E 64, 016132 (2001). snot defined for multigraphsc3s"|]}|ˆj|fVqdS(N(R(RR(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys sc3s&|]}ˆ|D] }|VqqdS(N((RR R(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys sigð?R'(RRRRRRR(RRRRRtsumR*R( R R RR#R R-R$R R.R/RR'((R s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pyRÍs$F      )  Gc shˆjƒrtjdƒ‚nˆjƒrBˆj}tjƒ}nˆj}tjƒ}|jj ˆjƒ|j ‡fd†|DƒƒxÚ|D]Ò}t ˆ|ƒ}t ‡fd†|Dƒƒt |gƒ}x|D]ˆ}t ||ƒ} |rt t || @ƒƒt || Bƒ} n/t t || @ƒƒtt |ƒt | ƒƒ} |j||d| ƒqÔWqŽW|S(s¶Overlap weighted projection of B onto one of its node sets. The overlap weighted projection is the projection of the bipartite network B onto the specified nodes with weights representing the Jaccard index between the neighborhoods of the two nodes in the original bipartite network [1]_: .. math:: w_{v,u} = \frac{|N(u) \cap N(v)|}{|N(u) \cup N(v)|} or if the parameter 'jaccard' is False, the fraction of common neighbors by minimum of both nodes degree in the original bipartite graph [1]_: .. math:: w_{v,u} = \frac{|N(u) \cap N(v)|}{min(|N(u)|,|N(v)|)} The nodes retain their attributes and are connected in the resulting graph if have an edge to a common node in the original bipartite graph. Parameters ---------- B : NetworkX graph The input graph should be bipartite. nodes : list or iterable Nodes to project onto (the "bottom" nodes). jaccard: Bool (default=True) Returns ------- Graph : NetworkX graph A graph that is the projection onto the given nodes. Examples -------- >>> from networkx.algorithms import bipartite >>> B = nx.path_graph(5) >>> G = bipartite.overlap_weighted_projected_graph(B, [0, 2, 4]) >>> print(G.nodes()) [0, 2, 4] >>> print(G.edges(data=True)) [(0, 2, {'weight': 0.5}), (2, 4, {'weight': 0.5})] >>> G = bipartite.overlap_weighted_projected_graph(B, [0, 2, 4], jaccard=False) >>> print(G.edges(data=True)) [(0, 2, {'weight': 1.0}), (2, 4, {'weight': 1.0})] Notes ------ No attempt is made to verify that the input graph B is bipartite. The graph and node properties are (shallow) copied to the projected graph. See Also -------- is_bipartite, is_bipartite_node_set, sets, weighted_projected_graph, collaboration_weighted_projected_graph, generic_weighted_projected_graph, projected_graph References ---------- .. [1] Borgatti, S.P. and Halgin, D. In press. Analyzing Affiliation Networks. In Carrington, P. and Scott, J. (eds) The Sage Handbook of Social Network Analysis. Sage Publications. snot defined for multigraphsc3s"|]}|ˆj|fVqdS(N(R(RR(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys ysc3s&|]}ˆ|D] }|VqqdS(N((RR R(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys |sR'(RRRRRRR(RRRRRR)R*tminR( R R tjaccardRR#R R-R$R R.R'((R s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pyR's&I      ) '/c s3ˆjƒrtjdƒ‚n|dkr6d„}nˆjƒrZˆj}tjƒ}nˆj}tjƒ}|j j ˆj ƒ|j ‡fd†|Dƒƒx|D]…}t ˆ|ƒ}t ‡fd†|Dƒƒt |gƒ}xC|D];}t ||ƒ} ||| ƒ} |j ||d| ƒqìWq¦W|S(sFWeighted projection of B with a user-specified weight function. The bipartite network B is projected on to the specified nodes with weights computed by a user-specified function. This function must accept as a parameter the neighborhood sets of two nodes and return an integer or a float. The nodes retain their attributes and are connected in the resulting graph if they have an edge to a common node in the original graph. Parameters ---------- B : NetworkX graph The input graph should be bipartite. nodes : list or iterable Nodes to project onto (the "bottom" nodes). weight_function: function This function must accept as a parameters two sets, the neighborhoods of two nodes, and return an integer or a float. The default function computes the number of shared neighbors. Returns ------- Graph : NetworkX graph A graph that is the projection onto the given nodes. Examples -------- >>> from networkx.algorithms import bipartite >>> def jaccard(unbrs, vnbrs): ... return float(len(unbrs & vnbrs)) / len(unbrs | vnbrs) ... >>> def shared(unbrs, vnbrs): ... return len(unbrs & vnbrs) ... >>> B = nx.path_graph(5) >>> G = bipartite.generic_weighted_projected_graph(B, [0, 2, 4], weight_function=jaccard) >>> print(G.nodes()) [0, 2, 4] >>> print(G.edges(data=True)) [(0, 2, {'weight': 0.5}), (2, 4, {'weight': 0.5})] >>> G = bipartite.generic_weighted_projected_graph(B, [0, 2, 4], weight_function=shared) >>> print(G.nodes()) [0, 2, 4] >>> print(G.edges(data=True)) [(0, 2, {'weight': 1}), (2, 4, {'weight': 1})] Notes ------ No attempt is made to verify that the input graph B is bipartite. The graph and node properties are (shallow) copied to the projected graph. See Also -------- is_bipartite, is_bipartite_node_set, sets, weighted_projected_graph, collaboration_weighted_projected_graph, overlap_weighted_projected_graph, projected_graph snot defined for multigraphscSst||@ƒS(N(R*(R-R.((s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pytËtc3s"|]}|ˆj|fVqdS(N(R(RR(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys Ósc3s&|]}ˆ|D] }|VqqdS(N((RR R(R (s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pys ÖsR'N(RRRtNoneRRRR(RRRRRR( R R tweight_functionRR#R R-R$R R.R'((R s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pyR†s&B        ) cCs t||ƒS(N(R(R R t create_using((s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pyRÝs(t__doc__tnetworkxRtjoint __author__t__all__RRRRRRR5RR(((s`/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/bipartite/projection.pyts     c V Z _ W