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 \(G=(V,E)\) 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

[R189]

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)