### Abstract

This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) model. We assume all nodes in the network are in the susceptible state initially, except one single information source that is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know the graph topology and all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample-path-based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for g+1 -regular trees such that gq > 1 , where g+1 is the node degree and q is the infection probability, the estimator is within a constant distance from the actual source with a high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic. We then further evaluate the performance of the reverse infection algorithm on several real-world networks.

Original language | English (US) |
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Journal | IEEE/ACM Transactions on Networking |

DOIs | |

State | Accepted/In press - Nov 20 2014 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Software
- Computer Science Applications
- Computer Networks and Communications

### Cite this

**Information Source Detection in the SIR Model : A Sample-Path-Based Approach.** / Zhu, Kai; Ying, Lei.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Information Source Detection in the SIR Model

T2 - A Sample-Path-Based Approach

AU - Zhu, Kai

AU - Ying, Lei

PY - 2014/11/20

Y1 - 2014/11/20

N2 - This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) model. We assume all nodes in the network are in the susceptible state initially, except one single information source that is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know the graph topology and all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample-path-based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for g+1 -regular trees such that gq > 1 , where g+1 is the node degree and q is the infection probability, the estimator is within a constant distance from the actual source with a high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic. We then further evaluate the performance of the reverse infection algorithm on several real-world networks.

AB - This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) model. We assume all nodes in the network are in the susceptible state initially, except one single information source that is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know the graph topology and all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample-path-based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for g+1 -regular trees such that gq > 1 , where g+1 is the node degree and q is the infection probability, the estimator is within a constant distance from the actual source with a high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic. We then further evaluate the performance of the reverse infection algorithm on several real-world networks.

UR - http://www.scopus.com/inward/record.url?scp=84911432372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84911432372&partnerID=8YFLogxK

U2 - 10.1109/TNET.2014.2364972

DO - 10.1109/TNET.2014.2364972

M3 - Article

AN - SCOPUS:84911432372

JO - IEEE/ACM Transactions on Networking

JF - IEEE/ACM Transactions on Networking

SN - 1063-6692

ER -