Agent-based models might be defined as a particular type of computational model aimed at simulating the behavior of autonomous agents and also their interactions under specific contextual conditions. In this methodological case study, a possible application of agent-based model is presented to study how minority ideas spread in society. Specifically, we will try to understand which are the social micro-mechanisms that permit the social contagion of minority opinions that are not publicly accepted. From this initial sociological concern, the case study is focused on the analysis of social processes of minority opinion spreading through four simulated scenarios. We aim to answer to three basic interrogates: (a) how the structure of social networks (i.e., network composition: types of nodes and number of links or edges) can affect the spread of minority opinion (network structure effect), (b) how committed or loyal agents can influence this process (opinion loyalty effect), and (c) how mass media action, as a contextual or environmental factor, might vary agents’ opinions and network composition. Results show that agent-based model may be a good alternative in social research when traditional methods are not suitable.