Graph-Theoretic Optimization for Edge Consensus

We consider network structures that optimize the H2-norm of weighted, time scaled consensus networks, under a minimal representation of such consensus networks described by the edge Laplacian. We show that a greedy algorithm can be used to find the minimum-H2 norm spanning tree, as well as how to choose edges to optimize the H2 norm when edges are added back to a spanning tree. In the case of edge consensus with a measurement model considering all edges in the graph, we show that adding edges between slow nodes in the graph provides the smallest increase in the H2 norm.