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networkx.algorithms.centrality.estrada_index

estrada_index(G)

Return the Estrada index of a the graph G.

The Estrada Index is a topological index of folding or 3D “compactness” ([1]).

Parameters:G (graph) Returns:estrada index Return type:float Raises:NetworkXError – If the graph is not undirected and simple.

Notes

Let G=(V,E) be a simple undirected graph with n nodes and let lambda_{1}leqlambda_{2}leqcdotslambda_{n} be a non-increasing ordering of the eigenvalues of its adjacency matrix A. The Estrada index is ([1], [2])

\[EE(G)=\sum_{j=1}^n e^{\lambda _j}.\]

References

[1]	(1, 2) E. Estrada, “Characterization of 3D molecular structure”, Chem. Phys. Lett. 319, 713 (2000). http://dx.doi.org/10.1016/S0009-2614(00)00158-5

[2]	José Antonio de la Peñaa, Ivan Gutman, Juan Rada, “Estimating the Estrada index”, Linear Algebra and its Applications. 427, 1 (2007). http://dx.doi.org/10.1016/j.laa.2007.06.020

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)