Return the Estrada index of a the graph G.

Parameters : G: graph estrada index: float NetworkXError If the graph is not undirected and simple.

Notes

Let $$G=(V,E)$$ be a simple undirected graph with $$n$$ nodes and let $$\lambda_{1}\leq\lambda_{2}\leq\cdots\lambda_{n}$$ 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)])