estrada_index¶

estrada_index(G)[source]¶

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

[R192]

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)