Fog computing is an interesting paradigm which has drawn attention recently, based on the presence of several Fog Nodes (FNs) able to interact among each other for sharing their tasks. To boost the interactions among FNs, an Energy-Aware Offloading Clustering Approach (EAOCA) is proposed for raising the network fairness in terms of FNs' energy level. In each cluster, there is a Fog Cluster Head (FCH) that aggregates the traffic from its Fog Cluster Members (FCMs) to be computed. EAOCA considers different policies for evaluating the impact of FCH and FCM selection and how the remained energy of the FNs influences the performance of the network in terms of fairness, delay and energy consumption. The simulation results later demonstrate how cluster updating frequency has a profound impact on the network lifetime.