TransitiveQ[g] yields True if graph g defines a transitive relation.

TreeIsomorphismQ[t_1, t_2] yields True if the trees t_1 and t_2 are isomorphic. It yields False otherwise.

TreeQ[g] yields True if graph g is a tree.

TriangleInequalityQ[g] yields True if the weights assigned to the edges of graph g satisfy the triangle inequality.

UndirectedQ[g] yields True if graph g is undirected.

UnweightedQ[g] yields True if all edge weights are 1 and False otherwise.

VertexCoverQ[g, c] yields True if the vertices in list c define a vertex cover of graph g.

Weak is an option to ConnectedQ that seeks to determine if a directed graph is weakly connected.

IntegerQuaternionQ[q] gives True if q is an integer quaternion and False otherwise.

QuaternionQ[q] gives True if q is a quaternion and False otherwise.