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The increasing penetration of smartphones, i.e., smart devices with multiple sensing and communication interfaces, creates the possibility to build novel types of networks. Wireless adaptors are, after the terminal screen, the strongest source of power consumption. It is therefore common for a node to occasionally turn off the networking device to save energy. The effect of the presence of nodes in the off-state must therefore be thoroughly evaluated. We propose an analytical model based on evolving graphs. Our proposal provides an exhaustive evaluation of an ideal routing protocol whose aim is to determine the worst case conditions when adopting a device switching-off strategy to save energy. The complexity of our algorithm is demonstrated to be O(nT2), n being the number of nodes, and T being the width of the time interval studied. We also show, through experimental results, that routing protocols for SWN must deal with 2 issues: a low percentage of delivered packets and with long paths.