With the rise of social media, political conversations now take place in more diffuse environments. In this context, it is not always clear why some actors, more than others, have greater influence on how discussions are shaped. To investigate the factors behind such influence, we build on nodality, a concept in political science which describes the capacity of an actor to exchange information within discourse networks. This concept goes beyond traditional network metrics that describe the position of an actor in the network to include exogenous drivers of influence (e.g. factors relating to organisational hierarchies). We study online discourse on Twitter (now X) in the UK to measure the relative nodality of two sets of policy actors - Members of Parliament (MPs) and accredited journalists - on four policy topics. We find that influence on the platform is driven by two key factors: (i) active nodality, derived from the actor's level of topic-related engagement, and (ii) inherent nodality, which is independent of the platform discourse and reflects the actor's institutional position. These findings significantly further our understanding of the origins of influence on social media platforms and suggest in which contexts influence is transferable across topics.