Abstract: The problem of sorting data is analyzed, the order relation between which is described as the adjacency relation of vertices on an arbitrary graph. Subtasks and issues related to the ‘neighborhood‘ of the problem are highlighted; their solution is the level of ‘immersion‘ in the solution of the general problem. Algorithms for solving individual subtasks for graphs of a special kind are discussed, as well as various approaches to solving the sorting problem in the general case. A sorting task of this type was proposed at the ISI-Junior School Programming Cup in July 2019 (Innopolis).