Machine learning and artificial intelligence are two key emerging technologies in computer science that require vast amounts of data for a meaningful application. The requirement of such a large dataset is usually met by pooling data from various sources, which is often difficult to implement in practice due to strict data privacy constraints. Peer-to-Peer federated learning is a distributed machine learning paradigm with a primary goal of learning a well-performing global model by collaboratively learning a shared model at different data hubs without the need of sharing data. Due to its immense practical applications, there is a growing attention towards various challenges of efficient fed- erated learning including communication efficiency, assumptions on connectivity, data heterogeneity, enhanced privacy, etc. In this paper, we address the communication efficiency of Peer-to-Peer federated learning, modeling it using a graph theoretical frame- work. We show that one can draw from a range of graph-based algorithms to construct an efficient communication algorithm on a connected network, thereby matching the inference efficiency of centralized federated learning as well as that of a consolidated dataset. We conduct experiments with varied graph formations and sizes to validate our claims.