Increasing evidence suggests that, similar to face-to-face communications, human emotions also spread in online social media. However, the mechanisms underlying this emotional contagion, for example, whether different feelings spread in unlikely ways or how the spread of emotions relates to the social network, is rarely investigated. Indeed, because of high costs and spatio-temporal limitations, explorations of this topic are challenging using conventional questionnaires or controlled experiments. Because they are collection points for natural affective responses of massive individuals, online social media sites offer an ideal proxy for tackling this issue from the perspective of computational social science. In this paper, based on the analysis of millions of tweets in Weibo, surprisingly, we find that anger is more contagious than joy, indicating that it can spark more angry follow-up tweets. Moreover, regarding dissemination in social networks, anger travels easily along weaker ties than joy, meaning that it can infiltrate different communities and break free of local traps because strangers share such content more often. Through a simple diffusion model, we reveal that greater contagion and weaker ties function cooperatively to speed up anger's spread. The diffusion of real-world events with different dominant emotions provides further testimony to the findings. To the best of our knowledge, this is the first time that quantitative long-term evidence has been presented that reveals a difference in the mechanism by which joy and anger are disseminated. Our findings shed light on both personal anger management in human communications and on controlling collective outrage in cyberspace.