Members of different political groups not only disagree about issues but also dislike and distrust each other. While social media can amplify this emotional divide -- called affective polarization by political scientists -- there is a lack of agreement on its strength and prevalence. We measure affective polarization on social media by quantifying the emotions and toxicity of reply interactions. We demonstrate that, as predicted by affective polarization, interactions between users with same ideology (in-group replies) tend to be positive, while interactions between opposite-ideology users (out-group replies) are characterized by negativity and toxicity. Second, we show that affective polarization generalizes beyond the in-group/out-group dichotomy and can be considered a structural property of social networks. Specifically, we show that emotions vary with network distance between users, with closer interactions eliciting positive emotions and more distant interactions leading to anger, disgust, and toxicity. Finally, we show that similar information exhibits different dynamics when spreading in emotionally polarized groups. These findings are consistent across diverse datasets spanning discussions on topics such as the COVID-19 pandemic and abortion in the US. Our research provides insights into the complex social dynamics of affective polarization in the digital age and its implications for political discourse.