### Abstract

Many important graph parameters can be expressed as eigen-functions of its adjacency matrix. Examples include epidemic threshold, graph robustness, etc. It is often of key importance to accurately monitor these parameters. For example, knowing that Ebola virus has already been brought to the US continent, to avoid the virus from spreading away, it is important to know which emerging connections among related people would cause great reduction on the epidemic threshold of the network. However, most, if not all, of the existing algorithms computing these measures assume that the input graph is static, despite the fact that almost all real graphs are evolving over time. In this paper, we propose two online algorithms to track the eigen-functions of a dynamic graph with linear complexity wrt the number of nodes and number of changed edges in the graph. The key idea is to leverage matrix perturbation theory to efficiently update the top eigen-pairs of the underlying graph without recomputing them from scratch at each time stamp. Experiment results demonstrate that our methods can reach up to 20 x speedup with precision more than 80% for fairly long period of time.

Original language | English (US) |
---|---|

Title of host publication | SIAM International Conference on Data Mining 2015, SDM 2015 |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 559-567 |

Number of pages | 9 |

ISBN (Print) | 9781510811522 |

State | Published - 2015 |

Event | SIAM International Conference on Data Mining 2015, SDM 2015 - Vancouver, Canada Duration: Apr 30 2015 → May 2 2015 |

### Other

Other | SIAM International Conference on Data Mining 2015, SDM 2015 |
---|---|

Country | Canada |

City | Vancouver |

Period | 4/30/15 → 5/2/15 |

### Fingerprint

### Keywords

- Attribution analysis
- Connectivity
- Dynamic graph
- Graph spectrum

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Vision and Pattern Recognition
- Software

### Cite this

*SIAM International Conference on Data Mining 2015, SDM 2015*(pp. 559-567). Society for Industrial and Applied Mathematics Publications.

**Fast eigen-functions tracking on dynamic graphs.** / Chen, Chen; Tong, Hanghang.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*SIAM International Conference on Data Mining 2015, SDM 2015.*Society for Industrial and Applied Mathematics Publications, pp. 559-567, SIAM International Conference on Data Mining 2015, SDM 2015, Vancouver, Canada, 4/30/15.

}

TY - GEN

T1 - Fast eigen-functions tracking on dynamic graphs

AU - Chen, Chen

AU - Tong, Hanghang

PY - 2015

Y1 - 2015

N2 - Many important graph parameters can be expressed as eigen-functions of its adjacency matrix. Examples include epidemic threshold, graph robustness, etc. It is often of key importance to accurately monitor these parameters. For example, knowing that Ebola virus has already been brought to the US continent, to avoid the virus from spreading away, it is important to know which emerging connections among related people would cause great reduction on the epidemic threshold of the network. However, most, if not all, of the existing algorithms computing these measures assume that the input graph is static, despite the fact that almost all real graphs are evolving over time. In this paper, we propose two online algorithms to track the eigen-functions of a dynamic graph with linear complexity wrt the number of nodes and number of changed edges in the graph. The key idea is to leverage matrix perturbation theory to efficiently update the top eigen-pairs of the underlying graph without recomputing them from scratch at each time stamp. Experiment results demonstrate that our methods can reach up to 20 x speedup with precision more than 80% for fairly long period of time.

AB - Many important graph parameters can be expressed as eigen-functions of its adjacency matrix. Examples include epidemic threshold, graph robustness, etc. It is often of key importance to accurately monitor these parameters. For example, knowing that Ebola virus has already been brought to the US continent, to avoid the virus from spreading away, it is important to know which emerging connections among related people would cause great reduction on the epidemic threshold of the network. However, most, if not all, of the existing algorithms computing these measures assume that the input graph is static, despite the fact that almost all real graphs are evolving over time. In this paper, we propose two online algorithms to track the eigen-functions of a dynamic graph with linear complexity wrt the number of nodes and number of changed edges in the graph. The key idea is to leverage matrix perturbation theory to efficiently update the top eigen-pairs of the underlying graph without recomputing them from scratch at each time stamp. Experiment results demonstrate that our methods can reach up to 20 x speedup with precision more than 80% for fairly long period of time.

KW - Attribution analysis

KW - Connectivity

KW - Dynamic graph

KW - Graph spectrum

UR - http://www.scopus.com/inward/record.url?scp=84961901889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961901889&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781510811522

SP - 559

EP - 567

BT - SIAM International Conference on Data Mining 2015, SDM 2015

PB - Society for Industrial and Applied Mathematics Publications

ER -