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, 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 of this index as the “Estrada index” was proposed by de la Peña et al. in 2007. Let formula_1 be a graph of size formula_2 and let formula_3 be a non-increasing ordering of the eigenvalues of its adjacency matrix formula_4. 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 formula_6 is defined as  The subgraph centrality has the following closed form  where formula_9 is the formula_6 th entry of the formula_11th eigenvector associated with the eigenvalue formula_12. It is straightforward to realise that