Geometric frustration is the standard explanation for reduced magnetization in quantum spin systems. Place antiferromagnetic spins on a triangular lattice: each spin wants to point opposite its neighbors, but three mutual neighbors cannot all point opposite each other. The frustration is geometric — the lattice topology prevents the ground state from satisfying all pairwise interactions simultaneously.
On complex networks — graphs with heterogeneous degree distributions, hubs, and community structure — the conventional frustration measures fail (arXiv:2403.09116). Total spin in quantum magnets on these networks is largely insensitive to frustration level. Systems with very different amounts of geometric frustration produce nearly identical magnetizations. The correlation between standard frustration indices and the ground state spin is negligible.
What matters instead is network heterogeneity. Hubs — nodes with many connections — dominate the magnetic behavior. A hub connected to many spins acts as a local field that aligns its neighbors regardless of frustration in the rest of the network. The hub's high degree means its local contribution to the total energy overwhelms the frustrated triangles elsewhere. Remove the hub, and the frustrated regions matter. Leave it, and they don't.
This is not a small correction. On lattices, frustration is the dominant effect — it determines whether the system is a ferromagnet, an antiferromagnet, or a spin liquid. On complex networks, frustration is secondary to topology. The same frustration index that predicts magnetic behavior on lattices predicts nothing on networks.
The distinction matters because real magnetic materials are not perfect lattices. Defects, disorder, grain boundaries, and compositional variation create effective network structures with heterogeneous connectivity. The lattice model's frustration-centric view may be systematically overweighting a feature whose importance depends on a structural regularity that real materials do not have.