  Behavior of hysteretic trajectories for cyclical input is investigated as a
function of the internal structure of a system modeled by the classical random
network of binary spins. Different regimes of hysteretic behavior are
discovered for different network connectivity and topology. Surprisingly,
hysteretic trajectories which do not converge at all are observed. They are
shown to be associated with the presence of specific topological elements in
the network structure, particularly with the fully interconnected spin groups
of size equal or greater than 4.
