Estrada has been a major contributor in the study of
complex networks, where he has developed several approaches to investigate the
network topology and
network dynamics. An index introduced by him in 1999 to characterize the degree of
protein folding, and then generalized to the study of
complex networks in 2005, is nowadays widely known as the
Estrada index of a graph or network. Estrada is also known in the field of
spectral graph theory where he has introduced several approaches to characterize the organizational architecture of
Complex networks, such as the "subgraph
centrality", "communicability", "spectral scaling", among others. His generalization of the
discrete Laplace operator, as the d-path Laplacians and their transforms, has opened several new avenues for studying long-range interactions in
network dynamics. Estrada is also known in the area of
mathematical chemistry, in particular for the development and use of
molecular descriptors based on the use of
Graph Theory. In recent years he has developed mathematical approaches for the
Hückel method or
tight binding model, such as for "graph energy", "
density matrix", "quantum molecular interference" in
molecular electronics, among others. The last work is in collaboration with
Roald Hoffmann. ==Awards and Distinctions==