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estrada_index

estrada_index(G)

Return the Estrada index of a the graph G.

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

See also

estrada_index_exp()

Notes

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

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

References

[1]	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)