### Abstract

Given the topology of a graph G and a budget κ, how can we quickly find the best κ edges to delete that minimize dissemination in G? Stopping dissemination in a graph is important in a variety of fields from epidemiology to cyber security. The spread of an entity (e.g., a virus) on an arbitrary graph depends on two properties: (1) the topology of the graph and (2) the characteristics of the entity. In many settings, we cannot manipulate the latter, such as the entity's strength. That leaves us with modifying the former (e.g., by removing nodes and/or edges from the graph in order to reduce the graph's connectivity). In this work, we address the problem of removing edges. We know that the largest eigenvalue of the graph's adjacency matrix is a good indicator for its connectivity (a.k.a. path capacity). Thus, algorithms that are able to quickly reduce the largest eigenvalue of a graph often minimize dissemination on that graph. However, a problem arises when the differences between the largest eigenvalues of a graph are small. This problem, known as the small eigen-gap problem, occurs often in social graphs such as Facebook postings or instant messaging (IM) networks. We introduce a scalable algorithm called MET (short for Multiple Eigenvalues Tracking), which efficiently and effectively solves the small eigen-gap problem. Our extensive experiments on different graphs from various domains show the efficacy and efficiency of our approach.

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 | 694-702 |

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

### 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. 694-702). Society for Industrial and Applied Mathematics Publications.

**MET : A fast algorithm for minimizing propagation in large graphs with small eigen-gaps.** / Le, Long T.; Eliassi-Rad, Tina; 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. 694-702, SIAM International Conference on Data Mining 2015, SDM 2015, Vancouver, Canada, 4/30/15.

}

TY - GEN

T1 - MET

T2 - A fast algorithm for minimizing propagation in large graphs with small eigen-gaps

AU - Le, Long T.

AU - Eliassi-Rad, Tina

AU - Tong, Hanghang

PY - 2015

Y1 - 2015

N2 - Given the topology of a graph G and a budget κ, how can we quickly find the best κ edges to delete that minimize dissemination in G? Stopping dissemination in a graph is important in a variety of fields from epidemiology to cyber security. The spread of an entity (e.g., a virus) on an arbitrary graph depends on two properties: (1) the topology of the graph and (2) the characteristics of the entity. In many settings, we cannot manipulate the latter, such as the entity's strength. That leaves us with modifying the former (e.g., by removing nodes and/or edges from the graph in order to reduce the graph's connectivity). In this work, we address the problem of removing edges. We know that the largest eigenvalue of the graph's adjacency matrix is a good indicator for its connectivity (a.k.a. path capacity). Thus, algorithms that are able to quickly reduce the largest eigenvalue of a graph often minimize dissemination on that graph. However, a problem arises when the differences between the largest eigenvalues of a graph are small. This problem, known as the small eigen-gap problem, occurs often in social graphs such as Facebook postings or instant messaging (IM) networks. We introduce a scalable algorithm called MET (short for Multiple Eigenvalues Tracking), which efficiently and effectively solves the small eigen-gap problem. Our extensive experiments on different graphs from various domains show the efficacy and efficiency of our approach.

AB - Given the topology of a graph G and a budget κ, how can we quickly find the best κ edges to delete that minimize dissemination in G? Stopping dissemination in a graph is important in a variety of fields from epidemiology to cyber security. The spread of an entity (e.g., a virus) on an arbitrary graph depends on two properties: (1) the topology of the graph and (2) the characteristics of the entity. In many settings, we cannot manipulate the latter, such as the entity's strength. That leaves us with modifying the former (e.g., by removing nodes and/or edges from the graph in order to reduce the graph's connectivity). In this work, we address the problem of removing edges. We know that the largest eigenvalue of the graph's adjacency matrix is a good indicator for its connectivity (a.k.a. path capacity). Thus, algorithms that are able to quickly reduce the largest eigenvalue of a graph often minimize dissemination on that graph. However, a problem arises when the differences between the largest eigenvalues of a graph are small. This problem, known as the small eigen-gap problem, occurs often in social graphs such as Facebook postings or instant messaging (IM) networks. We introduce a scalable algorithm called MET (short for Multiple Eigenvalues Tracking), which efficiently and effectively solves the small eigen-gap problem. Our extensive experiments on different graphs from various domains show the efficacy and efficiency of our approach.

UR - http://www.scopus.com/inward/record.url?scp=84961904764&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961904764&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781510811522

SP - 694

EP - 702

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

PB - Society for Industrial and Applied Mathematics Publications

ER -