Distributed algorithms are extremely useful in wireless sensor network to compute the global statistics using local computations. Periodic gossip algorithm is a distributed consensus algorithm, where neighbouring nodes gossip at every time instant. Convergence rate of periodic gossip algorithms determines the time sensor nodes will take to reach consensus. In this paper, we model the WSN as a r-nearest neighbour network and study the effect of nearest neighbours on convergence rate of the gossip algorithms. The ‘ r’ in nearest neighbour network models the node transmission radius and overhead in wireless sensor networks (WSN). We consider the both even and odd number of nodes and observe the convergence rate drastically increasing with the increase in the number of nearest neighbours until the network is fully connected.