Clustering is one of the widely used methods to save energy, increase spatial re usability, and scalability. In this paper, we have proposed a new fuzzy graph based modeling approach for wireless sensor network which takes into account the dynamic nature of network, volatile aspects of radio links and physical layer uncertainty. The fuzzy graph constructs fuzzy neighborhoods which are used to identify all the prospective member nodes of a cluster. For computation of optimum centrality of a cluster, we have defined a new centrality metric namely fuzzy k-hop centrality. The proposed centrality metric considers residual energy of individual nodes, link quality, hop distance between the prospective cluster head and respective member nodes to ensure better cluster head selection and cluster quality. Finally, a new computationally inexpensive clustering algorithm has been developed. The simulation results demonstrate that the proposed algorithm resulted in prolonged network lifetime in terms of clustering rounds, scalability, higher energy efficiency and uniform cluster head and cluster members distribution, as compare to LEACH-ERE and CHEF.