  The well-known regularity lemma of E. Szemer\'edi for graphs (i.e. 2-uniform
hypergraphs) claims that for any graph there exists a vertex partition with the
property of quasi-randomness. We give a simple construction of such a
partition. It is done just by taking a constant-bounded number of random vertex
samplings only one time (thus, iteration-free). Since it is independent from
the definition of quasi-randomness, it can be generalized very naturally to
hypergraph regularization. In this expository note, we show only a graph case
of the paper [I] on hypergraphs, but may help the reader to access [I].
