Abstract This paper presents the analysis of the performance of the consensus on regular network structures in information engineering. The consensus protocols introduced are distributed in the sense that each agent only needs information from its neighbors, which reduces the complexity of links between agents significantly. By graph Laplacian spectrum and frequency domain analysis, the performance of the consensus, characterized by the convergence rate and robustness to the communication constraints, are investigated in details. We establish direct connections between the system parameters and the performance of the consensus. Specifically, the convergence rates and the maximum fixed time-delays that can be tolerated by the various regular networks are found explicitly.