### Abstract

Our goal is to quickly find top $k$ lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find a node with the largest degree requires an average complexity of $\mbox{O}(n)$, 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 the 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 which requires very little knowledge about the structure of the network.

Original language | English |
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Place of Publication | Sophia Antipolis, France |

Publisher | INRIA |

Number of pages | 13 |

Publication status | Published - Feb 2012 |

### Publication series

Name | Research Report / INRIA, ISSN 0249-6399 |
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Publisher | INRIA |

No. | 7881 |

ISSN (Print) | 0249-6399 |

### Keywords

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

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## Cite this

Avrachenkov, K., Litvak, N., Sokol, M., & Towsley, D. (2012).

*Quick detection of nodes with large degrees*. (Research Report / INRIA, ISSN 0249-6399; No. 7881). Sophia Antipolis, France: INRIA.