has.loops returns TRUE iff x is allowed to contain loops (or loop-like edges, in the hypergraphic case).
is.directed returns TRUE iff the edges of x are to be interpreted as directed.
is.hyper returns TRUE iff x is allowed to contain hypergraphic edges.
is.multiplex returns TRUE iff x is allowed to contain multiplex edges.
References
Butts, C.T. 2002. ``Memory Structures for Relational Data in R: Classes and Interfaces'' Working Paper.