The current document is directed to methods and systems that determine whether or not two graph-like representations of two physically or temporally distinct computer systems or computer-system configurations are equivalent. The currently described methods and systems extract a first and second ordered set of subgraphs from each of a first and second graph-like representation of a first and a second computer system. The ordered sets of subgraphs are logically aligned, forming a set of subgraph pairs. The currently described methods and systems transform the first and second subgraph of each subgraph pair into a corresponding first and second set of trees, label the trees, and then compare labels at each level of the trees to determine whether or not an isomorphic tree can be found in the second set of trees for each tree in the first set of trees.
