networkx.algorithms.centrality.estrada_index¶

estrada_index(G)[source]¶

Returns the Estrada index of a the graph G.

The Estrada Index is a topological index of folding or 3D “compactness” (1).

Parameters: G (graph)
Returns: estrada index
Return type: float
Raises: 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}leqlambda_{2}leqcdotslambda_{n} be a non-increasing ordering of the eigenvalues of its adjacency matrix A. The Estrada index is (1, 2)

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

References

1(1,2): E. Estrada, “Characterization of 3D molecular structure”, Chem. Phys. Lett. 319, 713 (2000). https://doi.org/10.1016/S0009-2614(00)00158-5
2: José Antonio de la Peñaa, Ivan Gutman, Juan Rada, “Estimating the Estrada index”, Linear Algebra and its Applications. 427, 1 (2007). https://doi.org/10.1016/j.laa.2007.06.020

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)
>>> print(f"{ei:0.5}")
20.55