  We study field-driven dynamics of spins with antiferromagnetic interaction
along the links of a complex substrate geometry, which is modeled by graphs of
a controlled connectivity distribution. The magnetization reversal occurs in
avalanches of spin flips, which are pinned by the topological constraints of
the underlying graph. The hysteresis loop and avalanche sizes are analyzed and
classified in terms of graph's connectivity and clustering. The results are
relevant for magnets with a hierarchical spatial inhomogeneity and for design
of nanoscale magnetic devices.
