Stress Centrality of Some Graph Operations

Centrality measures are the tools used in most of the network analysis to rank the vertices of the network. Depending on different perspectives, many important centrality measures are defined and used for network analysis. Stress is one such important centrality measure of graphs applicable to the study of social and biological networks. Stress centrality evaluates the importance of a node by counting how many shortest paths pass through it. A node with higher stress centrality tends to be the one that plays a critical role in connecting different parts of the network, as it lies on a large number of shortest paths between other nodes. In this article, we obtain the stress centrality of vertices in the product graphs with reference to the unary operations, namely the splitting graph, the shadow graph, and the Mycielski graph. Further, we have given the expressions for the total stress of a few standard classes of graphs with respect to these operations.