Text might contain or invoke multiple emotions with varying intensities. As such, emotion detection, to predict multiple emotions associated with a given text, can be cast into a multi-label classification problem. We would like to go one step further so that a ranked list of relevant emotions are generated where top ranked emotions are more intensely associated with text compared to lower ranked emotions, whereas the rankings of irrelevant emotions are not important. A novel framework of relevant emotion ranking is proposed to tackle the problem. In the framework, the objective loss function is designed elaborately so that both emotion prediction and rankings of only relevant emotions can be achieved. Moreover, we observe that some emotions co-occur more often while other emotions rarely co-exist. Such information is incorporated into the framework as constraints to improve the accuracy of emotion detection. Experimental results on two real-world corpora show that the proposed framework can effectively deal with emotion detection and performs remarkably better than the state-of-the-art emotion detection approaches and multi-label learning methods.