Hyper stress index for graphs

Shimbel (1953) introduced the node centrality index, which is the stress of a vertex. The number of geodesics (shortest paths) that pass through a vertex in a graph is its stress. A number that links a chemical structure to physical characteristics or chemical reactivity is called a topological index of the chemical structure (graph). In this work, we present the Hyper stress index, a new topological index for graphs based on vertex stresses. Additionally, we compute the hyper stress index for a few standard graphs, prove a few results, and establish a few inequalities.