The embodiments herein provide a system and method for compact representation of graphs of regular degree. The graphs of regular degree are represented in a compact manner using a plurality of representation methods. The compact representation of the graphs of regular degree allows ease of understanding, storage and transmission of the graphs. The compact representation of graphs is a method for compression of graphs and representation of graphs with the minimum number of variables thereby enabling the storage and transmission of data in graph format efficiently. Further, the compact representation of graphs allows presentation of infinite family representation of Hamiltonian bipartite graphs of regular degree.