### Abstract

This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability q via the community. In the special case with q= 1 the model reduces to a random intersection graph which is known to generate high levels of transitivity also in the sparse context. The parameter q adds a degree of freedom and leads to a parsimonious and analytically tractable network model with tunable density, transitivity, and degree fluctuations. We prove that the parameters of this model can be consistently estimated in the large and sparse limiting regime using moment estimators based on partially observed densities of links, 2-stars, and triangles.

Original language | English |
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Title of host publication | Algorithms and Models for the Web Graphs |

Subtitle of host publication | 15th International Workshop, WAW 2018, Moscow, Russia, May 17-18, 2018, Proceedings |

Editors | A. Bonato, P. Pralat, A, Raigorodskii |

Place of Publication | Dordrecht |

Publisher | Springer |

Pages | 44-58 |

Number of pages | 15 |

ISBN (Electronic) | 978-3-319-92871-5 |

ISBN (Print) | 978-3-319-92870-8 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

Event | 15th Workshop on Algorithms and Models for the Web Graph, WAW 2018 - Moscow, Russian Federation Duration: 17 May 2018 → 18 May 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10836 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th Workshop on Algorithms and Models for the Web Graph, WAW 2018 |
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Country | Russian Federation |

City | Moscow |

Period | 17/05/18 → 18/05/18 |

### Fingerprint

### Cite this

*Algorithms and Models for the Web Graphs: 15th International Workshop, WAW 2018, Moscow, Russia, May 17-18, 2018, Proceedings*(pp. 44-58). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10836 LNCS). Dordrecht: Springer. https://doi.org/10.1007/978-3-319-92871-5_4

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*Algorithms and Models for the Web Graphs: 15th International Workshop, WAW 2018, Moscow, Russia, May 17-18, 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10836 LNCS, Springer, Dordrecht, pp. 44-58, 15th Workshop on Algorithms and Models for the Web Graph, WAW 2018, Moscow, Russian Federation, 17/05/18. https://doi.org/10.1007/978-3-319-92871-5_4

**Parameter estimators of sparse random intersection graphs with thinned communities.** / Karjalainen, Joona; van Leeuwaarden, Johan S.H.; Leskelä, Lasse.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Parameter estimators of sparse random intersection graphs with thinned communities

AU - Karjalainen, Joona

AU - van Leeuwaarden, Johan S.H.

AU - Leskelä, Lasse

PY - 2018/1/1

Y1 - 2018/1/1

N2 - This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability q via the community. In the special case with q= 1 the model reduces to a random intersection graph which is known to generate high levels of transitivity also in the sparse context. The parameter q adds a degree of freedom and leads to a parsimonious and analytically tractable network model with tunable density, transitivity, and degree fluctuations. We prove that the parameters of this model can be consistently estimated in the large and sparse limiting regime using moment estimators based on partially observed densities of links, 2-stars, and triangles.

AB - This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability q via the community. In the special case with q= 1 the model reduces to a random intersection graph which is known to generate high levels of transitivity also in the sparse context. The parameter q adds a degree of freedom and leads to a parsimonious and analytically tractable network model with tunable density, transitivity, and degree fluctuations. We prove that the parameters of this model can be consistently estimated in the large and sparse limiting regime using moment estimators based on partially observed densities of links, 2-stars, and triangles.

UR - http://www.scopus.com/inward/record.url?scp=85048231452&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-92871-5_4

DO - 10.1007/978-3-319-92871-5_4

M3 - Conference contribution

AN - SCOPUS:85048231452

SN - 978-3-319-92870-8

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

SP - 44

EP - 58

BT - Algorithms and Models for the Web Graphs

A2 - Bonato, A.

A2 - Pralat, P.

A2 - Raigorodskii, A,

PB - Springer

CY - Dordrecht

ER -