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