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estrada_index

estrada_index(G)

Return the Estrada index of a the graph G.

Parameters :

G: graph :

Returns :

estrada index: float :

Raises :

NetworkXError :

If the graph is not undirected and simple.

See also

estrada_index_exp

Notes

Let

System Message: WARNING/2 (G=(V,E))

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.
be a simple undirected graph with

System Message: WARNING/2 (n)

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.
nodes and let

System Message: WARNING/2 (\lambda_{1}\leq\lambda_{2}\leq\cdots\lambda_{n})

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.
be a non-increasing ordering of the eigenvalues of its adjacency matrix

System Message: WARNING/2 (A)

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 Estrada index is

System Message: WARNING/2 (EE(G)=\sum_{j=1}^n e^{\lambda _j}. )

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.

References

[R149]E. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett. 319, 713 (2000).

Examples

>>> G=nx.Graph([(0,1),(1,2),(1,5),(5,4),(2,4),(2,3),(4,3),(3,6)])
>>> ei=nx.estrada_index(G)