Stress in Directed Graphs: A Generalization of Graph Stress

In graph theory, centrality measures are used to identify the most important or influential nodes within a network. Stress centrality is one such measure, which helps quantify how "stressed" a node is within the overall graph structure based on the number of shortest paths that pass through it. Stress centrality provides a more thorough assessment of a node's relevance than other centrality metrics since it considers not only the direct connections of a node but also the indirect effects through its neighboring nodes. Furthermore, stress centrality can be applied to biological, technical, and social networks, among other kinds of networks. The idea of stress has been expanded from undirected graphs to directed graphs in our study. The stress on a vertex v in D is half of the number of geodesics passing through the vertex v, denoted by st(v). This definition reduces to the case of stress of undirected graph whenever the digraph is symmetric. We have some findings on the stress on a digraph as well as the stress on a vertex. A few standard digraphs' stresses are obtained, including the stress on any vertex in the cartesian product of digraphs, and some characterization on stress regular digraphs is made.