This paper sheds new light on the fundamental gap between graph-based models used by protocol designers and fading channel models used by communication theorists in wireless networks. The paper experimentally demonstrates that graph-based models capture real-world phenomena inadequately. Consequentially, it advocates studying models beyond graphs even for protocol-design. In the main part the paper presents an archetypal multi-hop situation. It shows that the theoretical limits of any protocol which obeys the laws of graph-based models can be broken by a protocol explicitly defined for the physical model. Finally, the paper discusses possible applications, from data gathering to media access control.
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