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Graph processing is an emerging computation model for a wide range of applications and graph partitioning is important for optimizing the cost and performance of graph processing jobs. In this paper, we propose a heterogeneous adaptive heuristic for geo-aware graph partitioning method which aims at minimizing the inter Data centre cost on data transfer time of graph processing jobs in geo-distributed DCs while satisfying the WAN usage budget. Heuristics can be multiple pass for graph processing. It is effective on assigning edges to different nodes. It adopts adaptive heuristics which address the challenges in WAN usage and network heterogeneities separately. Heuristics can be also applied to partition dynamic graphs minimize lightweight runtime overhead. Evaluation results show that proposed technique can reduce the inter-DC data transfer time by up to 78% and reduce the WAN usage by up to 80% compared to state-of-the-art graph partitioning methods with a low runtime overhead.