We extend the Contextual-Graphs formalism for modeling interaction in a group activity. Group activity is modeled as the cyclic traversing of a contextual meta-graph representing the group activity in terms of member activities, and of the shared context as a hub for interaction management. We propose a model of group-member interaction at the level of the transitions between turns. The model relies on the representation of members' activities in terms of independent tasks that are structured by simulation parameters in the shared context.