Securing multi-robot teams against malicious activity is crucial as these systems accelerate towards widespread societal integration. This emerging class of “physical networks” requires research into new methods of security that exploit their physical nature. This paper derives a theoretical framework for securing multi-agent consensus against the Sybil attack by using the physical properties of wireless transmissions. Our frame-work uses information extracted from the wireless channels to design a switching signal that stochastically excludes potentially untrustworthy transmissions from the consensus. Intuitively, this amounts to selectively ignoring incoming communications from untrustworthy agents, allowing for consensus to the true average to be recovered with high probability if initiated after a certain observation time T0that we derive. This work is different from previous work in that it allows for arbitrary malicious node values and is insensitive to the initial topology of the network so long as a connected topology over legitimate nodes in the network is feasible. We show that our algorithm will recover consensus and the true graph over the system of legitimate agents with an error rate that vanishes exponentially with time.