### Abstract

Extracting information from large graphs has become an important statistical problem since network data is now common in various fields. In this minicourse we will investigate the most natural statistical questions for three canonical probabilistic models of networks: (i) community detection in the stochastic block model, (ii) finding the embedding of a random geometric graph, and (iii) finding the original vertex in a preferential attachment tree. Along the way we will cover many interesting topics in probability theory such as Pólya urns, large deviation theory, concentration of measure in high dimension, entropic central limit theorems, and more.

Original language | English (US) |
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Pages (from-to) | 1-47 |

Number of pages | 47 |

Journal | Statistics Surveys |

Volume | 11 |

DOIs | |

State | Published - Jan 1 2017 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Keywords

- Community detection
- Evolving random graphs
- Networks
- Preferential attachment
- Random geometric graphs
- Random graphs
- Random trees
- Statistical inference
- Stochastic block model

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## Cite this

Rácz, M. Z., & Bubeck, S. (2017). Basic models and questions in statistical network analysis.

*Statistics Surveys*,*11*, 1-47. https://doi.org/10.1214/17-SS117