In this paper, we propose a Distributed Graph Model (DGM) and data structure to enable communicationaware heuristics in distributed load balancers (LBs). DGM is motivated by the desire to maintain and use information related to the affinity between tasks (their communication) in order to improve data locality while scheduling tasks in a distributed fashion to avoid the centralization overhead. Results show that DGM is able to achieve speedups of up to 50.4x with 40 virtual cores, when compared to a centralized graph representation with the same purpose. Additionally, we propose a proofof-concept distributed scheduler that uses DGM, named Edge Migration, and its implementation in the Charm++ parallel programming model. These results show that, although the communication analysis is much faster with DGM, it is still the most relevant overhead in distributed LBs. We also observe that Edge Migration has a decision time in the same order of magnitude as other communication-unaware decentralized algorithms. Thus, DGM can be used in communication-aware distributed LBs to improve load balancing decisions with a small impact in the overall LB performance.