The role of network topologies in designing a network is to define the arrangement of various components like devices, nodes, and connections within the infrastructure. Different topologies, such as star, ring, and mesh, dictate how data flows and how devices communicate within the network. Choosing the right topology impacts performance, scalability, fault tolerance, and complexity of network management. Understanding and implementing suitable network topologies is fundamental for ensuring efficient data transmission, optimizing resource use, and enhancing overall network reliability.