Communication is the main motive in any Networks whether it is Wireless Sensor Network, Ad-Hoc networks, Mobile Networks, Wired Networks, Local Area Network, Metropolitan Area Network, Wireless Area Network etc, hence it must be energy efficient. The main parameters for energy efficient communication are maximizing network lifetime, saving energy at the different nodes, sending the packets in minimum time delay, higher throughput etc. This paper focuses mainly on the energy efficient communication with the help of Adjacency Matrix in the Wireless Sensor Networks. The energy efficient scheduling can be done by putting the idle node in to sleep node so energy at the idle node can be saved. The proposed model in this paper first forms the adjacency matrix and broadcasts the information about the total number of existing nodes with depths to the other nodes in the same cluster from controller node. When every node receives the node information about the other nodes for same cluster they communicate based on the shortest depths and schedules the idle node in to sleep mode for a specific time threshold so energy at the idle nodes can be saved.