On the convergence of average consensus with generalized metropolis-hasting weights

Average consensus is a well-studied method for distributed averaging. The convergence properties of average consensus depend on the averaging weights. Examples for commonly used weight designs are Metropolis-Hastings (MH) weights and constant weights. In this paper, we provide a complete convergence analysis for a generalized MH weight design that encompasses conventional MH as special case. More specifically, we formulate sufficient and necessary conditions for convergence. A main conclusion is that AC with MH weights is guaranteed to converge unless the underlying network is a regular bipartite graph.