Before revision:  In this paper the average dynamics  is introduced as an heuristic tool to construct models of reaction networks with their qualitative properties explored in terms of connectivity properties of the Interaction Graphs for the ODEs, the Markov chain and the resulting average dynamics.
After revision:  In this paper the average dynamics is introduced as an heuristic tool to construct models of reaction or contact networks. The graphical concepts introduced form the basis for any subsequent study of the qualitative properties of hybrid models in terms of connectivity properties of the Interaction Graphs for the ODEs, the Markov chain and the resulting average dynamics.