## Abstract

We address the problem of estimating core numbers of nodes by reading edges of a large graph stored in external memory. The core number of a node is the highest k-core in which the node participates. Core numbers are useful in many graph mining tasks, especially ones that involve finding communities of nodes, influential spreaders and dense subgraphs. Large graphs often do not fit on the memory of a single machine. Existing external memory solutions do not give bounds on the required space. In practice, existing solutions also do not scale with the size of the graph. We propose NimbleCore, an iterative external-memory algorithm, which estimates core numbers of nodes using O(n log d_{max}) space, where n is the number of nodes and d_{max} is the maximum node-degree in the graph. We also show that NimbleCore requires O(n) space for graphs with power-law degree distributions. Experiments on forty-eight large graphs from various domains demonstrate that NimbleCore gives space savings up to 60X, while accurately estimating core numbers with average relative error less than 2.3%.

Original language | English (US) |
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Title of host publication | Proceedings of the 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 207-214 |

Number of pages | 8 |

ISBN (Electronic) | 9781509028467 |

DOIs | |

State | Published - Nov 21 2016 |

Event | 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2016 - San Francisco, United States Duration: Aug 18 2016 → Aug 21 2016 |

### Other

Other | 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2016 |
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Country | United States |

City | San Francisco |

Period | 8/18/16 → 8/21/16 |

## ASJC Scopus subject areas

- Computer Networks and Communications
- Sociology and Political Science
- Communication