# Encyclopedia of Database Systems

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

# Frequent Graph Patterns

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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1. 1.
Han J, Cheng H, Xin D, Yan X. Frequent pattern mining: current status and future directions. Data Min Knowl Disc. 2007;15(1):55–86.
2. 2.
Huan J, Prins J, Wang W, Carter C, Dokholyan NV. Coordinated evolution of protein sequences and structures with structure entropy. Technical Reports Computer Science Department; 2006.Google Scholar
3. 3.
Huan J, Wang W, Bandyopadhyay D, Snoeyink J, Prins J, Tropsha A. Mining protein family specific residue packing patterns from protein structure graphs. In: Proceedings of the 8th Annual International Conference on Research in Computational Molecular Biology; 2004. p. 308–15.Google Scholar
4. 4.
Huan J, Wang W, Prins J. Efficient mining of frequent subgraph in the presence of isomorphism. In: Proceedings of the 3rd IEEE International Conference on Data Mining; 2003. p. 549–52.Google Scholar
5. 5.
Huan J, Wang W, Prins J, Yang J. SPIN: mining maximal frequent subgraphs from graph databases. In: Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; 2004. p. 581–6.Google Scholar
6. 6.
Inokuchi A, Washio T, Motoda H. An apriori-based algorithm for mining frequent substructures from graph data. In: Principles of Data Mining and Knowledge Discovery, 4th European Conference; 2000. p. 13–23.
7. 7.
Kuramochi M., Karypis G. Frequent subgraph discovery. In: Proceedings of the 1st IEEE International Conference on Data Mining; 2001. p. 313–20.Google Scholar
8. 8.
Nijssen S, Kok J. A quickstart in frequent structure mining can make a difference. In: Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; 2004.p. 647–52.Google Scholar
9. 9.
Smalter A, Huan J, Lushington G. Structure-based pattern mining for chemical compound classification. In: Proceedings of the 6th Asia Pacific Bioinformatics Conference; 2008. p. 39–48.Google Scholar
10. 10.
Vanetik N, Gudes E. Mining frequent labeled and partially labeled graph patterns. In: Proceedings of the 20th International Conference on Data Engineering; 2004. p. 91–102.Google Scholar
11. 11.
Yan X, Han J. gSpan: graph-based substructure pattern mining. In: Proceedings of the 2nd IEEE International Conference on Data Mining; 2002. p. 721–4.Google Scholar