These-days Wireless Sensor Networks (WSNs) has become integral part of many applications include tracking, monitoring and so on. Nodes are limited in battery, memory and processing capacity. Tracking and monitoring applications continue to work for longer hours; energy is the major constraint for network to transmit sensed data. State of the art specifies that by using clustering method energy-efficiency, scalability, and efficient-data-communication is achieved. Sensors deployed in the network be partitioned to clusters then one of the nodes is designated to become a Cluster Head (CH) that accumulate sensed information and sends to Sink/Base Station (BS). Normally CH is elected by considering nodes remaining energy and topological attributes related to the node in network. In this projected clustering method a centrality-metric “Cluster-Optimal-Degree-Centrality (CODC)”, is defined and also considered other parameters residual energy, distance between CHs, plus number of nodes belonging to a cluster guarantees better cluster configuration and CH selection. Fuzzy-Inference-System takes Expected-Residual-Energy (ERE) and CODC as inputs. Experiments are carried using ns-2; the proposed clustering method improves QoS, and efficiently prolongs network lifetime.