overlap_weighted_projected_graph
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Newman’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 [R123]:
System Message: WARNING/2 (w_{v,u} = \sum_k \frac{\delta_{v}^{w} \delta_{w}^{k}}{k_w - 1})
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System Message: WARNING/2 (v)
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latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.13 (TeX Live 2013/dev) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, lo aded. (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty (/usr/share/texlive/texmf-dist/tex/latex/ucs/utf8x.def)) (/usr/share/texlive/texmf-dist/tex/latex/ucs/ucs.sty (/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-global.def)) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) (/usr/share/texlive/texmf-dist/tex/latex/tools/bm.sty) ! LaTeX Error: File `preview.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.12 \begin {document}^^M No pages of output. Transcript written on math.log.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
nodes : list or iterable
|
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Returns : | Graph : NetworkX graph
|
See also
is_bipartite, is_bipartite_node_set, sets, weighted_projected_graph, overlap_weighted_projected_graph, generic_weighted_projected_graph, projected_graph
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.
References
[R123] | (1, 2) Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality, M. E. J. Newman, Phys. Rev. E 64, 016132 (2001). |
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})