Estrada index
Introduction 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  be a graph of size  and let  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:  The subgraph centrality has the following closed form:  where   is the  th entry of the  th eigenvector associated with the eigenvalue . It is straightforward to realise that:
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