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We propose representation of configurational physical quantities andmicroscopic structures for multicomponent system on lattice, by extending aconcept of generalized Ising model (GIM) to graph theory. We construct graphLaplacian (and adjacency matrix) composed of symmetry-equivalent neighboringedges, whose landscape of spectrum explicitly represents GIM description ofstructures as well as low-dimensional topological information in terms ofgraph. The proposed representation indicates the importance of linearcombination of graph to further investigate the role of spatial constraint onequilibrium properties in classical systems. We demonstrate that spectrum forsuch linear combination of graph can find out additional characteristicmicroscopic structures compared with GIM-based descriptions for given set offigures on the same low-dimensional configuration space, coming from theproposed representation explicitly having more structural information for e.g.,higher-order closed links of selected element. Statistical interdependence fordensity of microscopic states including graph representation for structures isalso examined, which exhibits similar behavior that has been seen for GIMdescription of the microscopic structures.

Graph Representation for Configurational Properties of Crystalline Solids