### Abstract

We define a distance of two graphs that reflects the closeness of both local and global properties, We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a symmetric measurable function in two variables. We use these notions of distance and graph limits to give a general theory for parameter testing. As examples, we provide short proofs of the testability of MaxCut and the recent result of Alon and Shapira about the testability of hereditary graph properties.

Original language | English |
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Title of host publication | Proceedings of the Annual ACM Symposium on Theory of Computing |

Pages | 261-270 |

Number of pages | 10 |

Volume | 2006 |

Publication status | Published - 2006 |

Event | 38th Annual ACM Symposium on Theory of Computing, STOC'06 - Seattle, WA, United States Duration: May 21 2006 → May 23 2006 |

### Other

Other | 38th Annual ACM Symposium on Theory of Computing, STOC'06 |
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Country | United States |

City | Seattle, WA |

Period | 5/21/06 → 5/23/06 |

### Fingerprint

### Keywords

- Convergence of graphs
- Distance of graphs
- Graph homomorphism
- Graph limit
- Property testing

### ASJC Scopus subject areas

- Software

### Cite this

*Proceedings of the Annual ACM Symposium on Theory of Computing*(Vol. 2006, pp. 261-270)

**Graph limits and parameter testing.** / Borgs, Christian; Chayes, Jennifer; Lovász, L.; Sós, Vera T.; Szegedy, Balázs; Vesztergombi, Katalin.

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

*Proceedings of the Annual ACM Symposium on Theory of Computing.*vol. 2006, pp. 261-270, 38th Annual ACM Symposium on Theory of Computing, STOC'06, Seattle, WA, United States, 5/21/06.

}

TY - GEN

T1 - Graph limits and parameter testing

AU - Borgs, Christian

AU - Chayes, Jennifer

AU - Lovász, L.

AU - Sós, Vera T.

AU - Szegedy, Balázs

AU - Vesztergombi, Katalin

PY - 2006

Y1 - 2006

N2 - We define a distance of two graphs that reflects the closeness of both local and global properties, We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a symmetric measurable function in two variables. We use these notions of distance and graph limits to give a general theory for parameter testing. As examples, we provide short proofs of the testability of MaxCut and the recent result of Alon and Shapira about the testability of hereditary graph properties.

AB - We define a distance of two graphs that reflects the closeness of both local and global properties, We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a symmetric measurable function in two variables. We use these notions of distance and graph limits to give a general theory for parameter testing. As examples, we provide short proofs of the testability of MaxCut and the recent result of Alon and Shapira about the testability of hereditary graph properties.

KW - Convergence of graphs

KW - Distance of graphs

KW - Graph homomorphism

KW - Graph limit

KW - Property testing

UR - http://www.scopus.com/inward/record.url?scp=33748103148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748103148&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33748103148

SN - 1595931341

SN - 9781595931344

VL - 2006

SP - 261

EP - 270

BT - Proceedings of the Annual ACM Symposium on Theory of Computing

ER -