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estrada_index(G)

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

Notes

Let :None:None:`G=(V,E)` be a simple undirected graph with :None:None:`n` nodes and let :None:None:`\lambda_{1}\leq\lambda_{2}\leq\cdots\lambda_{n}` be a non-increasing ordering of the eigenvalues of its adjacency matrix :None:None:`A`. The Estrada index is (, )

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

Parameters

G: graph :

Raises

NetworkXError

If the graph is not undirected and simple.

Returns

estrada index: float

Returns the Estrada index of a the graph G.

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
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.centrality.subgraph_alg.estrada_index

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /networkx/algorithms/centrality/subgraph_alg.py#293
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