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, 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.

Derivation

Let G=(V,E) be a graph of size |V|=n and let be a non-increasing ordering of the eigenvalues of its adjacency matrix A. 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 i is defined as The subgraph centrality has the following closed form where is the i th entry of the jth eigenvector associated with the eigenvalue \lambda _j. It is straightforward to realise that