Mathematica can use multiple internal representations for
Graphs. Normally, we don't need to care about this. But the specific representation used can influence the performance of some functions, and is relevant to understanding some bugs and coming up with useful workarounds.
The graph representation can be queried with
repr = GraphComputation`GraphRepresentation[g]
and set with
What are the possible values of
repr and when can (or can't) they be used?