Graph pattern mining methods can extract informative and useful patterns from large-scale graphs and capture underlying principles through the overwhelmed information. Contrast analysis serves as a keystone in various fields and has demonstrated its effectiveness in mining valuable information. However, it has been long overlooked in graph pattern mining. Therefore, in this paper, we introduce the concept of contrast subgraph, that is, a subset of nodes that have significantly different edges or edge weights in two given graphs of the same node set. The major challenge comes from the gap between the contrast and the informativeness. Because of the widely existing noise edges in real-world graphs, the contrast may lead to subgraphs of pure noise. To avoid such meaningless subgraphs, we leverage the similarity as the cornerstone of the contrast. Specifically, we first identify a coherent core, which is a small subset of nodes with similar edge structures in the two graphs, and then induce contrast subgraphs from the coherent cores. Moreover, we design a general family of coherence and contrast metrics and derive a polynomial-time algorithm to efficiently extract contrast subgraphs. Extensive experiments verify the necessity of introducing coherent cores as well as the effectiveness and efficiency of our algorithm. Real-world applications demonstrate the tremendous potentials of contrast subgraph mining.