n-metrics for multiple graph alignment
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The work of Ioannidis et al. 2018 introduces a family of distances between two graphs that provides tractable graph alignment strategies. Importantly, the alignment scores produced by this family satisfy the properties of metrics, which is very useful in several learning tasks. In this paper, we generalize this work to compare n graphs by introducing a family of distances, which is an n-metric, i.e., an extension of a metric to n elements that includes a generalization of the triangle inequality. Our new family of distances, includes the ones in the work of Ioannidis et al. 2018 as a special case, and can produce tractable alignments between multiple graphs.
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