This paper provides the technical details of an article originally published in The Conversation in February 2020. The purpose is to use centrality measures to analyse the social network of movie stars and thereby identify the most "important" actors in the movie business. The analysis is presented in a step-by-step, tutorial-like fashion and makes use of the Python programming language together with the NetworkX library. It reveals that the most central actors in the network are those with lengthy acting careers, such as Christopher Lee, Nassar, Sukumari, Michael Caine, Om Puri, Jackie Chan, and Robert De Niro. We also present similar results for the movie releases of each decade. These indicate that the most central actors since the turn of the millennium include people like Angelina Jolie, Brahmanandam, Samuel L. Jackson, Nassar, and Ben Kingsley.