Estrada index

In chemical graph theory, the Estrada index is a topological index of protein folding.

The index was first defined by Ernesto Estrada as a measure of the degree of folding of a protein,[1] which is represented as a path-graph weighted by the dihedral or torsional angles of the protein backbone.

This index of degree of folding has found multiple applications in the study of protein functions and protein-ligand interactions.

The name "Estrada index" was introduced by de la Peña et al. in 2007.

be a graph of size

be a non-increasing ordering of the eigenvalues of its adjacency matrix

The Estrada index is defined as For a general graph, the index can be obtained as the sum of the subgraph centralities of all nodes in the graph.

The subgraph centrality of node

is defined as[3] The subgraph centrality has the following closed form[3] where