This paper investigates a class of linear multi-agent network systems, in which nodes are coupled by dynamic edges in the sense that each edge has a dynamic system attached as well. The outputs of the edge dynamic systems form the external inputs of the node dynamic systems, which are termed neighboring inputs representing the coupling actions between nodes. The outputs of the node dynamic systems are the inputs of the edge dynamic systems. Several cooperative output regulation problems are posed, including output synchronization, output cooperation and master-slave output cooperation. Output cooperation is specified as making the neighboring input, a weighted sum of edge outputs, track a predefined trajectory by cooperation of node outputs. Distributed cooperative output regulation controllers depending on local states and neighboring inputs are presented, which are designed by combining feedback passivity theories and the internal model principle. A simulation example on the cooperative current control of an electrical network illustrates the potential applications of the analytical results. Crown Copyright (C) 2016 Published by Elsevier Ltd. All rights reserved.