  We propose representation of configurational physical quantities and
microscopic structures for multicomponent system on lattice, by extending a
concept of generalized Ising model (GIM) to graph theory. We construct graph
Laplacian (and adjacency matrix) composed of symmetry-equivalent neighboring
edges, whose landscape of spectrum explicitly represents GIM description of
structures as well as low-dimensional topological information in terms of
graph. The proposed representation indicates the importance of linear
combination of graph to further investigate the role of spatial constraint on
equilibrium properties in classical systems. We demonstrate that spectrum for
such linear combination of graph can find out additional characteristic
microscopic structures compared with GIM-based descriptions for given set of
figures on the same low-dimensional configuration space, coming from the
proposed representation explicitly having more structural information for e.g.,
higher-order closed links of selected element. Statistical interdependence for
density of microscopic states including graph representation for structures is
also examined, which exhibits similar behavior that has been seen for GIM
description of the microscopic structures.
