  We quantify the emergent complexity of quantum states near quantum critical
points on regular 1D lattices, via complex network measures based on quantum
mutual information as the adjacency matrix, in direct analogy to quantifying
the complexity of EEG/fMRI measurements of the brain. Using matrix product
state methods, we show that network density, clustering, disparity, and
Pearson's correlation obtain the critical point for both quantum Ising and
Bose-Hubbard models to a high degree of accuracy in finite-size scaling for
three classes of quantum phase transitions, $Z_2$, mean field superfluid/Mott
insulator, and a BKT crossover.
