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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