Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Frequent Graph Patterns

  • Jun Huan
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_168

Synonyms

Graph database mining

Definition

There are three key concepts in mining graph databases: (i) labeled graph, (ii) subgraph isomorphism, and (iii) graph support value. Based on the concepts, the problem of frequent subgraph mining could be defined in the following discussion.

Definition 1

Alabeled graphG is a quadrupleG = (V, E, Σ, λ) where V is a set of vertices or nodes and EV × V is a set of undirected edges. Σ is a set of (disjoint) vertex and edge labels, and λ: V ∪ E → Σ is a function that assigns labels to vertices and edges. Typically a total ordering is defined on the labels in Σ.

With the previous definition, a graph database is a set of labeled graphs.

Definition 2

A graph G ′ = ( V′, E′, Σ′, λ′) is subgraph isomorphic to G = ( V, E, Σ, λ), denoted by G ′ ⊆ G, if there exists a 1–1 mapping f: V ′ → V such that
$$ \forall v\in V^{\prime },\uplambda^{\prime }(v)=\uplambda \left(f(v)\right) $$
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Recommended Reading

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of KansasLawrenceUSA

Section editors and affiliations

  • Jian Pei
    • 1
  1. 1.School of Computing ScienceSimon Fraser Univ.BurnabyCanada