The response speed of a network impacts the efficacy of its actions to external stimuli. However, for a given bound on the update rate, the network-response speed is limited by the need to maintain stability. This work increases the network-response speed without having to increase the update rate by using delayed self-reinforcement (DSR), where each agent uses its already available information from the network to strengthen its individual update law. Example simulation results are presented that show more than an order of magnitude improvement in the response speed (quantified using the settling time) with the proposed DSR approach.