  Phase transitions (PTs) are generally classified into second-order and
first-order transitions, each exhibiting different intrinsic properties. For
instance, a first-order transition exhibits latent heat and hysteresis when a
control parameter is increased and then decreased across a transition point,
whereas a second-order transition does not. Recently, hybrid percolation
transitions (HPTs) are issued in diverse complex systems, in which the features
of first-order and second-order PTs occur at the same transition point. Thus,
the question whether hysteresis appears in an HPT arises. Herein, we
investigate this fundamental question with a so-called restricted
Erd\H{o}s--R\'enyi random network model, in which a cluster fragmentation
process is additionally proposed. The hysteresis curve of the order parameter
was obtained. Depending on when the reverse process is initiated, the shapes of
hysteresis curves change, and the critical behavior of the HPT is conserved
throughout the forward and reverse processes.
