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The topology of ad hoc networks is critical in determining the performance of routing algorithms, capacity and lifetime of ad hoc networks. In this paper, we study the impact of different signal propagation models on topology, routing and lifetime of ad hoc networks. Moreover, we also study shortest path routing based on metrics such as distance and hopcount. Our analysis shows that shortest path routing based on hopcount leads to a better load balancing than shortest path routing based on distance. However, the lifetime of network increases when distance is used as a metric for shortest path routing.