This study examines how combinatorial analysis may address network optimization challenges via line graph creation. Line graphs, which can transform graphs, underpin graph theory. Points in a line graph indicate the first graph’s edges. Using this modification, we examine how network configurations might be improved for efficiency, cost reduction, and resource utilization. We tackle power, information, and transportation network challenges via line graph creation. The study uses theory and real-world examples to demonstrate how line graphs may simplify network optimization. It also discusses line graphs’ computational advantages for huge networks and their potential usage in IoT and smart communities. Line graphs may improve network systems in many combinatorial circumstances, as shown by the findings.