Fast Consensus Topology Design via Minimizing Laplacian Energy*

This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These constructed graphs possess maximum vertex and edge connectivity, and more importantly, generically exhibit large algebraic connectivity of an optimal order provided they are not sparse. These properties guarantee fast and resilient consensus processes over these graphs.