1. An administration-and-management component of a computer system comprising: one or more processors; one or more memories; one or more graph databases; and computer instructions stored in the one or more memories that, when executed by one or more of the one or more processors, control the computer-system administration-and-management component, on behalf of a calling computational entity, to store a first graph and a second graph that each represents a computer system in one or more of the one or more graph databases, each graph comprising a set of nodes and a set of edges, each node associated with two or more attribute values, each edge connecting two nodes, and each edge associated with two or more attribute values; determine whether or not the first and second graphs are equivalent by extracting two or more sets of subgraphs from each of the first and second graphs, each set of subgraphs extracted from the first graph corresponding to a complementary set of subgraphs extracted from the second graph, each subgraph extracted from a graph by selecting edges from the graph having one or more common values for each of one or more attributes associated with the edges and selecting nodes from the graph interconnected by the selected edges, transforming the subgraphs in the sets of subgraphs into trees within corresponding sets of trees, labeling nodes of the trees in the corresponding sets of trees, comparing labels at each level of trees selected from the sets of trees to generate a return value stored in one of the one or more memories, and returning the generated return value to the calling computational entity.