  A new graph-based order parameter is introduced for the characterization of
atomistic structures. The order parameter is universal to any material/chemical
system, and is transferable to all structural geometries. Three sets of data
are used to validate both the generalizability and accuracy of the algorithm:
(1) liquid lithium configurations spanning up to 300 GPa, (2) condensed phases
of carbon along with nanotubes and buckyballs at ambient and high temperature,
and (3) a diverse set of aluminum configurations including surfaces, compressed
and expanded lattices, point defects, grain boundaries, liquids, nanoparticles,
all at non-zero temperatures. The aluminum configurations are also compared to
existing characterization methods for both speed and accuracy. Our order
parameter uniquely classifies every configuration and outperforms all
crystalline order parameters studied here, opening the door for its use in a
multitude of complex application spaces that can require fine configurational
characterization of materials.
