The paper proposes to consider the positional value of a cooperative game on the graph as a measure of vertex centrality of the graph. A cooperative game on a graph with restricted cooperation is considered. The characteristic function of a cooperative game takes into account the number of paths of a given length within the coalition. A proposition about a positional value in a cooperative game with a characteristic function of a special form is formulated. An algorithm, that uses generating functions to find the number of paths of a given length passing through a certain vertex, has been adapted for finding a positional value. The results are illustrated by an example.