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This paper deals with an evolutionary graph network, which represents cooperative and competitive form in the multi-agent systems. We focus on the functional relationship or connectivity of the graph structure, rather than the physical configuration of itself. Each node corresponding to the agent has a variable number of links to the neighborhood nodes, dependent on the internal state and local interactions characterized as activation and inhibition. A simple collective game is considered to exemplify that evolutionary mechanisms of reconfiguration of the graph structure enhances cooperation form.