Eccentricity Centrality of the Comb Product Between Well-Known Graphs and Interval Graphs: Applications in Warehouse Network Optimisation

Abstract

In network analysis, measuring centrality is essential for determining the relative importance of each vertex within a network. A vertex 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 matter within the framework of calculating vertex eccentricities to ascertain the comparative importance of nodes within the network 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 a well-known graph and an interval graph, and we design two O(n) time algorithms—one for finding the eccentricity of all 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 a central warehouse in a warehouse network of an online product-selling company based on our study results.