The day before yesterday I talked to Alexander Rahm, whom I got to know by a drawing of his on a blackboard in the Übungssaal, that represented the modular graph. I was extremely nervous about that and inquired to find out who had written that.
He pointed me to some very interesting literature (Brown) that I can use as a reference. Also he remarked, that the modular graph is also called "Serre's graph" which to google returned many more results.
Also, he made it quite clear, that I should concentrate more on subgroups, since the modular group itself is very well understood. So, I'm trying to adapt my theory to $\Gamma^2$, $\Gamma^3$ and the commutator subgroup. It is kind of late to begin with a new dev cycle, but I fear it will be necessary, as the lack of treatment of subgroups always loomed over the whole thing.
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