Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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),
...     ]
... )
>>> 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