Graph labeling methods are necessary in addressing complex matters in a Mobile Ad- Hoc Network (MANET) such as connectivity, scaling, routing, and modeling the network. We can make measurements reasonably confident by structuring networks in the form of graphs, by representing them using matrices and by considering mathematical graph theory as the foundational analytical basis. The management of the network will be automated by algorithms, whereas simulating the networks are basic elements of networks, node density, node mobility, and link formation as well as packet routing in relation to the random graph theory. The research of congestion analysis of MANETs can be analyzed using various algorithms, all of which initially dwell on the principles of the graph theory. In this paper, certain programming of MATLAB will be introduced to investigate how 3-equity prime cordial labeling acts in cycle graphs with twin chords, and hence it may clarify the intricate dynamics of a MANET.