This dataset contains examples of graphs comparing rigidity concepts for generic bar-joint frameworks and for marble graphs. A marble graph is the contact graph of a collection of unit spheres in dimension three with non-overlapping interiors. For each graph there is a Graph6 file format and a list of edges in Mathematica notation. We also provide the coordinates that give the unit-distances (also in Mathematica format). The names of the files indicate the rigidity properties of the given graph.