estrada_index

estrada_index(G)[source]

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)