Close binary stars are binary stars where the component stars are close enough such that they can exchange mass and/or energy. They are subdivided into semidetached, overcontact, or ellipsoidal binary stars. A challenging problem in the context of close binary stars is their classification into these subclasses based solely on their light curves. Conventionally, this is done by observing subtle features in the light curves like the depths of adjacent minima, which is tedious when dealing with large datasets. In this work, we suggest the use of machine learning algorithms applied to quantifiers derived from recurrence networks to differentiate between classes of close binary stars. We show that overcontact binary stars occupy a region different from semidetached and ellipsoidal binary stars in a plane of characteristic path length and average clustering coefficient, computed from their recurrence networks. We use standard clustering algorithms and report that the clusters formed correspond to the standard classes with a high degree of accuracy.