I have some ideas about implementing graph connectives. I think that the best way to implement first four binary operations (union, join, intersection and difference) is to use adjacency matrices.
I think variants of these algorithms for non-adjacency matrices are just as important. It would be best to focus on these problems and their generic solution than to propose more solutions for a smaller set of graphs.
OK, let it be so. The implementation of graph connectives using the adjacency matrices isn't too difficult. Regarding adjacency lists or incidency matrices, it's more difficult and intererestring to perform such operations. I meant that it's more convenient to do the operations for adjacency matrices and then to convert them into another graph representation, but now I doubt that this will be more effective (it needs some time to convert a graph from one representation to another (and a lot of memory), and the algorithm needs time and memory, too).