We consider consensus networks whose nodes are integrators and whose edges are 2- tuples of real rational functions representing dynamical systems that couple the nodes. We review salient points from graph theory, including Laplacians, interconnection matrices, and consensus protocols, all of which typically involve constructs with static weights. We then generalize these notions to the case of graphs with integrating nodes and dynamic edges. We give conditions under which such graphs admit consensus, meaning that in the steady-state the node variables converge to a common value. The ideas are illustrated an example that motivated this work:
the modeling of thermal processes in buildings.