## Abstract

Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected. This paper discusses the estimation of these parameters from a single observed instance of the graph, using moment estimators based on observed degrees and frequencies of 2-stars and triangles. The observed data set is assumed to be a subgraph induced by a set of

*n*nodes sampled from the full set of n nodes. We prove the consistency of the proposed estimators by showing that the relative estimation error is small with high probability for_{0}*n*. As a byproduct, our analysis confirms that the empirical transitivity coefficient of the graph is with high probability close to the theoretical clustering coefficient of the model._{0}≫ n^{2/3}≫ 1Original language | English |
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Title of host publication | Algorithms and Models for the Web Graph |

Subtitle of host publication | 14th International Workshop, WAW 2017, Toronto, ON, Canada, June 15–16, 2017, Revised Selected Papers |

Editors | Anthony Bonato, Fan Chung Graham, Paweł Prałat |

Pages | 1–15 |

ISBN (Electronic) | 9783319678108 |

DOIs | |

Publication status | Published - 6 Sep 2017 |

MoE publication type | A4 Article in a conference publication |

Event | Workshop on Algorithms and Models for the Web Graph - Fields Institute for Research in Mathematical Sciences, Toronto, Canada Duration: 15 Jun 2017 → 16 Jun 2017 Conference number: 14 http://www.math.ryerson.ca/waw2017/index.html |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 10519 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Workshop

Workshop | Workshop on Algorithms and Models for the Web Graph |
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Abbreviated title | WAW |

Country/Territory | Canada |

City | Toronto |

Period | 15/06/2017 → 16/06/2017 |

Internet address |

## Keywords

- statistical network model
- network motif
- model fitting
- sparse graph
- moment estimator
- two-mode network
- overlapping communities