We construct new complementary sequence sets of size 4, using a graphical description. We explain how the construction can be seen as a special case of a less explicit array construction by Parker and Riera and, at the same time, a generalization of another construction by the same authors. Some generalizations of the construction are also given, which are not in the construction of Parker and Riera. Lower bounds and upper bounds of the number of sequences in the constructions are analyzed.