Many brands have entered the realm of social media as part of their marketing strategies. Nevertheless, on many occasions due to mishandling these interactions devolved into conflict which may scale rapidly and turn low intensity situations into crisis events. This presentation analyses conflicts in social media networks, fusing conflict map models with social network analysis such as graph analysis. The research is particularly focused on the Twitter platform, and is illustrated with cases from retail and travel categories. The methodology application can provide insights leading to control and neutralize conflicts in a fast and efficient way, enhancing consumers' rapport and confidence.