  Chung, Graham, and Wilson proved that a graph is quasirandom if and only if
there is a large gap between its first and second largest eigenvalue. Recently,
the authors extended this characterization to k-uniform hypergraphs, but only
for the so-called coregular k-uniform hypergraphs. In this paper, we extend
this characterization to all k-uniform hypergraphs, not just the coregular
ones. Specifically, we prove that if a k-uniform hypergraph satisfies the
correct count of a specially defined four-cycle, then there is a gap between
its first and second largest eigenvalue.
