### Abstract

Given a large graph, like a computer communication network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? This problem, referred to as the node immunization problem, is the core building block in many high-impact applications, ranging from public health, cybersecurity to viral marketing. A central component in node immunization is to find the best k bridges of a given graph. In this setting, we typically want to determine the relative importance of a node (or a set of nodes) within the graph, for example, how valuable (as a bridge) a person or a group of persons is in a social network. First of all, we propose a novel 'bridging' score Δλ, inspired by immunology, and we show that its results agree with intuition for several realistic settings. Since the straightforward way to compute Δλ is computationally intractable, we then focus on the computational issues and propose a surprisingly efficient way (O(nk^{2}+m) ) to estimate it. Experimental results on real graphs show that (1) the proposed 'bridging' score gives mining results consistent with intuition; and (2) the proposed fast solution is up to seven orders of magnitude faster than straightforward alternatives.

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

Article number | 7181715 |

Pages (from-to) | 113-126 |

Number of pages | 14 |

Journal | IEEE Transactions on Knowledge and Data Engineering |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

### Fingerprint

### Keywords

- graph mining
- Immunization
- scalability

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Information Systems
- Computer Science Applications

### Cite this

*IEEE Transactions on Knowledge and Data Engineering*,

*28*(1), 113-126. [7181715]. https://doi.org/10.1109/TKDE.2015.2465378

**Node Immunization on Large Graphs : Theory and Algorithms.** / Chen, Chen; Tong, Hanghang; Prakash, B. Aditya; Tsourakakis, Charalampos E.; Eliassi-Rad, Tina; Faloutsos, Christos; Chau, Duen Horng.

Research output: Contribution to journal › Article

*IEEE Transactions on Knowledge and Data Engineering*, vol. 28, no. 1, 7181715, pp. 113-126. https://doi.org/10.1109/TKDE.2015.2465378

}

TY - JOUR

T1 - Node Immunization on Large Graphs

T2 - Theory and Algorithms

AU - Chen, Chen

AU - Tong, Hanghang

AU - Prakash, B. Aditya

AU - Tsourakakis, Charalampos E.

AU - Eliassi-Rad, Tina

AU - Faloutsos, Christos

AU - Chau, Duen Horng

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Given a large graph, like a computer communication network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? This problem, referred to as the node immunization problem, is the core building block in many high-impact applications, ranging from public health, cybersecurity to viral marketing. A central component in node immunization is to find the best k bridges of a given graph. In this setting, we typically want to determine the relative importance of a node (or a set of nodes) within the graph, for example, how valuable (as a bridge) a person or a group of persons is in a social network. First of all, we propose a novel 'bridging' score Δλ, inspired by immunology, and we show that its results agree with intuition for several realistic settings. Since the straightforward way to compute Δλ is computationally intractable, we then focus on the computational issues and propose a surprisingly efficient way (O(nk2+m) ) to estimate it. Experimental results on real graphs show that (1) the proposed 'bridging' score gives mining results consistent with intuition; and (2) the proposed fast solution is up to seven orders of magnitude faster than straightforward alternatives.

AB - Given a large graph, like a computer communication network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? This problem, referred to as the node immunization problem, is the core building block in many high-impact applications, ranging from public health, cybersecurity to viral marketing. A central component in node immunization is to find the best k bridges of a given graph. In this setting, we typically want to determine the relative importance of a node (or a set of nodes) within the graph, for example, how valuable (as a bridge) a person or a group of persons is in a social network. First of all, we propose a novel 'bridging' score Δλ, inspired by immunology, and we show that its results agree with intuition for several realistic settings. Since the straightforward way to compute Δλ is computationally intractable, we then focus on the computational issues and propose a surprisingly efficient way (O(nk2+m) ) to estimate it. Experimental results on real graphs show that (1) the proposed 'bridging' score gives mining results consistent with intuition; and (2) the proposed fast solution is up to seven orders of magnitude faster than straightforward alternatives.

KW - graph mining

KW - Immunization

KW - scalability

UR - http://www.scopus.com/inward/record.url?scp=84961625682&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961625682&partnerID=8YFLogxK

U2 - 10.1109/TKDE.2015.2465378

DO - 10.1109/TKDE.2015.2465378

M3 - Article

AN - SCOPUS:84961625682

VL - 28

SP - 113

EP - 126

JO - IEEE Transactions on Knowledge and Data Engineering

JF - IEEE Transactions on Knowledge and Data Engineering

SN - 1041-4347

IS - 1

M1 - 7181715

ER -