From EG: I think probably the best way to start is, yes, with k-graph homology, and with an example in mind. As I said in an earlier email, I think the first question is: Does k-graph insplitting preserve k-graph homology? So, I would start by picking one of the examples of insplitting from EFGGGP, and compute the k-graph homology (as defined in KumjianPaskSimsHomology, Section 7, or equivalently in Gillaspy-Wu Section 3).

1. RP k-graph master file
2. rp k graphs