The impact of multi‐group multi‐layer network structure on the performance of distributed consensus building strategies

We consider a structural approach to the consensus building problem in multi‐group multi‐layer (MGML) distributed sensor networks (DSNs) common in many natural and engineering applications. From among the possible network structures, we focus on bipartite graph structure as it represents a typical MGML structure and has a wide applicability in the real world. We establish exact conditions for consensus and derive a precise relationship between the consensus value and the degree distribution of nodes in a bipartite MGML DSN. We also demonstrate that for subclasses of connectivity patterns, convergence time and simple characteristics of network topology can be captured by explicit algebra. Direct inference of the convergence behavior of consensus strategies from MGML DSN structure is the main contribution of this paper. The insights gained from our analysis facilitate the design and development of large‐scale DSNs that meet specific performance criteria. Copyright © 2012 John Wiley & Sons, Ltd.