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We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via multi-scale network analysis. The method is based on "community detection" wherein interacting particles are partitioned into an "ideal gas" of optimally decoupled groups of particles. Specifically, we construct a set of network representations ("replicas") of the physical system based on interatomic potentials and apply a multiscale clustering ("multiresolution community detection") analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time separation), or iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A(80)B(20) , a ternary model system with components "A", "B", and "C" in ratios of A(88)B(7)C(5) (as in Al(88)Y(7)Fe(5) , and to atomic coordinates in a Zr(80)Pt(20) system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length scale increases as the system becomes progressively rigid.

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering