Achieving empathy is a crucial step toward humanized dialogue systems. Current approaches for empathetic dialogue generation mainly perceive an emotional label to generate an empathetic response conditioned on it, which simply treat emotions independently, but ignore the intrinsic emotion correlation in dialogues, resulting in inaccurate emotion perception and unsuitable response generation. In this paper, we propose a novel emotion correlation enhanced empathetic dialogue generation framework, which comprehensively realizes emotion correlation learning, utilization, and supervising. Specifically, a multi-resolution emotion graph is devised to capture context-based emotion interactions from different resolutions, further modeling emotion correlation. Then we propose an emotion correlation enhanced decoder, with a novel correlation-aware aggregation and soft/hard strategy, respectively improving the emotion perception and response generation. Experimental results on the benchmark dataset demonstrate the superiority of our model in both empathetic perception and expression.