With increased 5G deployments, network densification is higher than ever to support the exponentially high throughput requirements. However, this has meant a significant increase in energy consumption, leading to higher operational expenditure (OpEx) for network operators creating an acute need for improvements in network energy savings (NES). A key determinant of operational efficacy in cellular networks is the user association (UA) policy, as it affects critical aspects like spectral efficiency, load balancing etc. and therefore impacts the overall energy consumption of the network directly. Furthermore, with cellular network topologies lending themselves well to graphical abstractions, use of graphs in network optimization has gained significant prominence. In this work, we propose and analyze a graphical abstraction based optimization for UA in cellular networks to improve NES by determining when energy saving features like cell switch off can be activated. A comparison with legacy approaches establishes the superiority of the proposed approach.