Computing services, when provided by Edge Networks rather than centralized clouds, are delivered close to the geographically extreme user edge. Edge computing enables functional offloading and improved scalability but suboptimal design of edge networks can result in needlessly high energy consumption and mismanagement of resources. Thus, how to effectively minimize the power dissipation of network resources at the edge is a significant problem as networks evolve. This thesis investigates a complete suite of energy efficient solution for the edge network. A frequency scalable router architecture, based on the Software Defined Network (SDN) concept, has been proposed. Two new control policies have been integrated with the proposed green architecture and their performance has been analysed to evaluate the trade-offs between energy efficiency and performance in frequency-scaled Network Devices. A Network Device Power Model (NDPM) has been formulated to explore the power dissipation characteristics of frequency scalable CMOS devices (as measured using a NetFPGA testbed). An Online Energy-efficient Resource Allocation model (OERA) has been designed based on this model. This allocation model can map the resource requests onto a substrate network in the edge, with concurrent consideration of multiple factors including geographical location, resource availability and network-level energy cost, etc. The model features better support of virtual resource requests and lower power consumption than existing solutions.