This paper addresses the issue of fake news detection, with a particular focus on solutions derived from graph theory. It covers identifying channels, which are sources of fake news, and identifying users spreading false information, considering users deliberately misleading their audience, forming clusters called 'troll farms'. It proposes a solution using graph theory, which includes classifying users based on the social context extracted in graph centrality measures built from user interactions or networks built from followers on the social network Twitter. The solution includes not only the identification of trolls but also potential unintentional users spreading false information, users exposed to false information, or automated scripts spreading information (bots). Thorough research on the efficiency of different features and classifiers is conducted on MIB and FakeNewsNet datasets. Conducted research confirms general conclusions from previous studies and offers some improvements.