Eccentricity centrality of the comb product between well-knowngraphs and interval graphs

In network analysis, measuring centrality is essential for determining the relative importance of each vertex with in a network. Avertex with higher centrality signifies greater importance compared to others. To facilitate theoretical studies, networks are commonly modelled using graphs. Deoxyribonucleic Acid (DNA) molecules, some scheduling problems, and food webs have a common linear structure that can be modelled as interval graphs. We explore this matterwithin the framework of calculating vertex eccentricities to ascertain the comparative importance of nodes within thenetwork structure. Eccentricity centrality plays an important role in identifying significant vertices in social networks,facility location networks, etc. In this paper, we compute the eccentricity centrality of the comb product between awell-known graph and an interval graph, and we design twoO(n)time algorithms—one for finding the eccentricity ofall vertices of the interval graph and another for making a Breadth-First Search (BFS) tree of interval graph. We also compute the eccentricity centrality of the comb product between two interval graphs using these algorithms. We also analyse the time complexity of the proposed algorithms. Finally, we present a real application involving in finding acentral warehouse in a warehouse network of an online product-selling company based on our study results.