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Graph support measures and flows

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Abstract

Graph databases have gained popularity in recent years because many data use graphs as easy and intuitive representations. The task of Graph Mining focuses on identifying statistically significant subgraphs, called patterns, in graph databases. This task has two parts: the search procedure itself, coupled with the help of a chosen support measure to evaluate the statistical significance of graph patterns. In this paper, we focus on the single-graph setting, where the database is a single large graph. We prove that all proper graph support measures correspond to flows in the network of instances, which provides the means for future classification of these measures.

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Notes

  1. The third part of this definition—one that is usually given in textbooks and requires that \(f(u,v)=-f(v,u)\)—is redundant. Moreover, this condition can only be used in networks where the Lovász path switching operation (Lovász 1976) does not change flow size. For instance, this requirement does not hold when a network has three distinct source-sink pairs.

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  1. Department of Software Engineering, Shamoon Academic College of Engineering, Bialik 56, 84100, Beer Sheva, Israel

    Natalia Vanetik

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  1. Natalia Vanetik
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Correspondence to Natalia Vanetik.

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Vanetik, N. Graph support measures and flows. Soc. Netw. Anal. Min. 12, 120 (2022). https://doi.org/10.1007/s13278-022-00955-z

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