In this article, we extend our understanding of fringe politics to include relational and thematic elements, namely, the relationship of far-right collective actors with their broader network and the claims made within it. Locating our analysis at the intersection of protest event and social network analysis, we focus on the far-right Movement for a Better Hungary (Jobbik) which, since late 2013, has committed to moderation. Analysing the protest events in which Jobbik took part and the types of claims upon which it has mobilized between 2009 and 2017, we examine whether there has been a corresponding distancing from extremist groups and radical claims – a finding that would indeed validate the substantive transformation of Jobbik. By focusing on often neglected relational and thematic aspects, the study provides new ways to analyse fringe collective actors, the relationship with their environment and the evolution of such a relationship over time.