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Operating the Internet infrastructure in an energy-efficient manner ("Green Internet") becomes a challenging issue in most recent years with the recognition of significant energy consumption due to its large scale. Yet a limited number of contributions are available to address the issue mainly through putting idle routers and links into sleep mode, at the price of low global resource utilization efficiency and degraded network performance. This paper follows the same line of research but investigates an optimal solution of configuring IP network topology to minimize the number of active routers and links, and hence energy consumption, whilst keep the interference on network operation minimal. An optimal energy-efficient network model along with a heuristic algorithm is proposed for identifying the network elements in sleep mode to attain approximately the best trade-off between the energy-efficiency and performance degradation. Numerical experiments are carried out to assess the solution for a range of network and load scenarios and the results clearly demonstrate its effectiveness.