### Abstract

For an undirected graph G without self-loop, we prove: (i) that the number of closed patterns in the adjacency matrix of G is even; (ii) that the number of the closed patterns is precisely double the number of maximal complete bipartite subgraphs of G; (iii) that for every maximal complete bipartite subgraph, there always exists a unique pair of closed patterns that matches the two vertex sets of the subgraph. Therefore, we can enumerate all maximal complete bipartite subgraphs by using efficient algorithms for mining closed patterns which have been extensively studied in the data mining field.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 146-156 |

Number of pages | 11 |

Volume | 3721 LNAI |

State | Published - 2005 |

Externally published | Yes |

Event | 9th European Conference on Principles and Practice of Knowledge Discovery in Databases, PKDD 2005 - Porto, Portugal Duration: Oct 3 2005 → Oct 7 2005 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 3721 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 9th European Conference on Principles and Practice of Knowledge Discovery in Databases, PKDD 2005 |
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Country | Portugal |

City | Porto |

Period | 10/3/05 → 10/7/05 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 3721 LNAI, pp. 146-156). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3721 LNAI).

**A correspondence between maximal complete bipartite subgraphs and closed patterns.** / Li, Jinyan; Li, Haiquan; Soh, Donny; Wong, Limsoon.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 3721 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3721 LNAI, pp. 146-156, 9th European Conference on Principles and Practice of Knowledge Discovery in Databases, PKDD 2005, Porto, Portugal, 10/3/05.

}

TY - GEN

T1 - A correspondence between maximal complete bipartite subgraphs and closed patterns

AU - Li, Jinyan

AU - Li, Haiquan

AU - Soh, Donny

AU - Wong, Limsoon

PY - 2005

Y1 - 2005

N2 - For an undirected graph G without self-loop, we prove: (i) that the number of closed patterns in the adjacency matrix of G is even; (ii) that the number of the closed patterns is precisely double the number of maximal complete bipartite subgraphs of G; (iii) that for every maximal complete bipartite subgraph, there always exists a unique pair of closed patterns that matches the two vertex sets of the subgraph. Therefore, we can enumerate all maximal complete bipartite subgraphs by using efficient algorithms for mining closed patterns which have been extensively studied in the data mining field.

AB - For an undirected graph G without self-loop, we prove: (i) that the number of closed patterns in the adjacency matrix of G is even; (ii) that the number of the closed patterns is precisely double the number of maximal complete bipartite subgraphs of G; (iii) that for every maximal complete bipartite subgraph, there always exists a unique pair of closed patterns that matches the two vertex sets of the subgraph. Therefore, we can enumerate all maximal complete bipartite subgraphs by using efficient algorithms for mining closed patterns which have been extensively studied in the data mining field.

UR - http://www.scopus.com/inward/record.url?scp=33646425029&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646425029&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33646425029

SN - 3540292446

SN - 9783540292449

VL - 3721 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 146

EP - 156

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -