Molecular dynamics simulation on uniquely labeled digraphs

There are 6 different types of molecules in the system, the reactions are according to Gamma(6,4) and Gamma(6,6) (a cycle with shortcut from node 1 to node 4 and 6 respectively).
Each moment a random event is chosen with equal probability ( a molecule of type 1 arrives in the system, a reaction happens, or a molecule of random type leaves the system [proportionally to concentration levels]).




Clearly molecule 1 gets a boost by the input, and those molecules that are products of more than one reactions (incoming edges) have higher concentrations, the others barely survive. The group structure is different in the above systems, but that does not seem to play any role. The dynamics is explained by the graph structure.

Ensemble dynamics: If at one moment the same reaction is applied to all molecules in the system, then the distribution of the molecules regarding their type is unimodal (i.e. at a moment only one type of molecule can be observed, the others' frequency is negligible), where the peak moves between the types reaction by reaction.

Witthout input and output flow: The stabilised concentration can be predicted by a simple graph algorithm (or something similar as the output may depened on where we start)

1. Start with value 1.
2. Go through the nodes from 2 to 1 cyclically and give the nodes the current value if there is one incoming edge, double if there are two, divide by 2 if there is a branch.

This should be a straightforward problem in the theory of flows on graphs.