In Wireless multimedia sensor networks (WMSNs), two graphs, communication network graph and vision graph, can be established. The camera nodes connected in the vision graph share overlapped field of views (FOVs) and they depend on the densely deployed relay nodes in the communication network graph to communicate with each other. Given a uniformly deployed camera sensor network with relay nodes, the problem is to find the number of hops for the vision-graph- neighbor-searching messages to construct the vision graph in an energy efficient way. In this paper, mathematical models are developed to analyze the FOV overlap of the camera nodes and the multi-hop communications in two dimensional topologies, which are utilized to analyze the optimal hop number. In addition, simulations are conducted to verify our models.
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