The representation of a system as a graph, where the vertices represent atoms and the edges represent the links between them, is widely used in chemistry and crystallography. The permutational symmetries of the system form the graph automorphism group, i.e., they preserve the edge-vertex connectivity. Consequently, the graph representation reduces the problem of finding symmetries in a system to finding elements of an automorphism group, a well-studied problem in the field of graph theory. However, building a representative graph encompassing the symmetries in a given relatively complex system along its finite temperature evolution is not straightforward. This work proposes a procedure for constructing such graph representation that describes an entire dataset of configurations rather than one particular structure.