Given a set of attributed subgraphs known to be from different classes, how can we discover their differences? There are many cases where collections of subgraphs may be contrasted against each other. For example, they may be assigned ground truth labels (spam/not-spam), or it may be desired to directly compare the biological networks of different species or compound networks of different chemicals. In this work we introduce the problem of characterizing the differences between attributed subgraphs that belong to different classes. We define this characterization problem as one of partitioning the attributes into as many groups as the number of classes, while maximizing the total attributed quality score of all the given subgraphs. We show that our attribute-to-class assignment problem is NP-hard and an optimal $(1 - 1/e)$-approximation algorithm exists. We also propose two different faster heuristics that are linear-time in the number of attributes and subgraphs. Unlike previous work where only attributes were taken into account for characterization, here we exploit both attributes and social ties (i.e. graph structure). Through extensive experiments, we compare our proposed algorithms, show findings that agree with human intuition on datasets from Amazon co-purchases, Congressional bill sponsorships, and DBLP co-authorships. We also show that our approach of characterizing subgraphs is better suited for sense-making than discriminating classification approaches.
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