The development of peer to peer overlay networks applications has attracted an immense interest from the research community in recent years. Several challenging issues have to be resolved in order to provide accessible, efficient and scalable inter-peer communication. Achieving resilience so as to reduce the disconnection probability, is among the most demanding issues to provide a robust and omnipresent service to peer to peer applications. This paper attempts to address this issue, by proposing a graph-theoretic model using the well-known star interconnection network with sub-logarithmic degree characteristics, which not only facilitate scalability problem, but also achieves maximum connectivity compared to the other existing graph-based methods. The simulation results confirm that the proposed solution attains a higher degree of resiliency compared to other existing topologies.