### Abstract

Our goal is to find top-$k$ lists of nodes with the largest degrees in large complex networks quickly. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find the top-$k$ list of nodes with the largest degrees requires an average complexity of $\mathcal{O}(n)$ , where $n$ is the number of nodes in the network. Even this modest complexity can be very high for large complex networks. We propose to use a random-walk-based method. We show theoretically and by numerical experiments that for large networks, the random-walk method finds good-quality top lists of nodes with high probability and with computational savings of orders of magnitude. We also propose stopping criteria for the random-walk method that requires very little knowledge about the structure of the network.

Original language | English |
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Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Internet mathematics |

Volume | 10 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 5 May 2014 |

### Keywords

- Random walk
- Detection of nodes with the largest degrees
- Stopping criteria
- Top $k$ list
- Complex networks

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## Cite this

Avrachenkov, K., Litvak, N., Sokol, M., & Towsley, D. (2014). Quick detection of nodes with large degrees.

*Internet mathematics*,*10*(1-2), 1-19. https://doi.org/10.1080/15427951.2013.798601