Are there any graph theory problems that could be solved by a lone, run-of-the-mill computer programmer as a side hobby?

I am thinking of a modest app that allows a simple graph to be drawn, and a selection of properties that can be searched for in the on-screen graph, e.g., bipartite, hasClique, etc.

If enough of these properties can be implemented, then collections of properties could be sought.

Eventually there would be an algorithm(s) to gradually construct graphs, and at each iteration in the construction process, some collection of properties can be sought for in the graph so far.

My question is has all this been done already by teams of commercial programmers, so that, at best this would just be self-educational?