Static stabilization of a decentralized discrete-time single-integrator network that is subject to Markovian variation in the communication/sensing topology is considered. In particular, we develop sufficient conditions on the Markovian topology for mean-square stabilization using a decentralized static controller that has no knowledge of the underlying Markov state. Our analysis exposes a deep connection between decentralized control of single-integrator networks with Markovian topology and those with fixed topology: static stabilization of the network with Markovian topology is possible whenever the steady-state time-average of the Markovian topology is amenable to static (fixed-topology-based) decentralized control. (c) 2005 Elsevier Ltd. All rights reserved.