  We consider quasirandom properties for Cayley graphs of finite abelian
groups. We show that having uniform edge-distribution (i.e., small discrepancy)
and having large eigenvalue gap are equivalent properties for such Cayley
graphs, even if they are sparse. This positively answers a question of Chung
and Graham ["Sparse quasi-random graphs", Combinatorica 22 (2002), no. 2,
217-244] for the particular case of Cayley graphs of abelian groups, while in
general the answer is negative.
