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 ${\displaystyle G=(V,E)}$ be a graph of size ${\displaystyle |V|=n}$ and let ${\displaystyle \lambda _{1}\geq \lambda _{2}\geq \cdots \geq \lambda _{n}}$ be a non-increasing ordering of the eigenvalues of its adjacency matrix ${\displaystyle A}$. The Estrada index is defined as

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