Functional analysis on hypergraphs: Density and zeta functions – applications to molecular graphs and image analysis

Abstract

This paper introduces new descriptors and invariants for hypergraphs. We develop a new type of Zeta functions and density functions, that are proved to have useful invariance and monotony properties. Links with hypergraph entropies are established as well. New matrices linked with hypergraphs are also proposed, from which a new type of Laplacian associated with hypergraphs is derived. Two applications are then suggested, molecular graphs in chemistry and image analysis, where the proposed functions and invariants are useful characterizations.