Maximum Common Subelement Metrics and its Applications to Graphs

In this paper we characterize a mathematical model called Maximum Common Subelement (MCS) Model and prove the existence of four different metrics on such model. We generalize metrics on graphs previously proposed in the literature and identify new ones by showing three different examples of MCS Models on graphs based on (1) subgraphs, (2) induced subgraphs and (3) an extended notion of subgraphs. This latter example can be used to model graphs with complex labels (e.g., graphs whose labels are other graphs), and hence to derive metrics on them. Furthermore, we also use (3) to show that graph edit distance, when a metric, is related to a maximum common subelement in a corresponding MCS Model.