A wireless sensor network is composed of a large number of tiny sensor nodes that can be deployed in a variety of environments like battle fields, water, large fields, and the like, and can transmit data to a Base station (BS). In a clusterbased network organization, sensor nodes are organized into clusters and one sensor node is selected as a sensor head (SH) in each cluster. Each SH denotes a facility and sends useful information to the Base Station (BS) through other SHs via the shortest path. In this paper, we study two clustering techniques, namely kmedian clustering and k-center clustering for a wireless sensor network. All the sensor nodes are static and homogeneous (having the same specifications) and SHs are assumed to be heterogeneous with respect to other sensor nodes in their respective clusters (but homogeneous to other SHs once they are located). The focus of this paper is to compare the k-median and k-center clustering techniques based on shortest path and total intra-cluster distance. We have implemented the two clustering techniques using the Java language and necessary experimental and statistical results are provided.