Rumors in a Network: Who's the Culprit?
We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with the popular susceptible-infected (SI) model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2014
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| Online Access: | http://hdl.handle.net/1721.1/88122 https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0003-4973-9343 |
| _version_ | 1826196017828069376 |
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| author | Shah, Devavrat Zaman, Tauhid R. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Shah, Devavrat Zaman, Tauhid R. |
| author_sort | Shah, Devavrat |
| collection | MIT |
| description | We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with the popular susceptible-infected (SI) model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term rumor centrality. We establish that this is a maximum likelihood (ML) estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has nontrivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops of the true source across different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding rumor sources in networks which are not tree-like. |
| first_indexed | 2024-09-23T10:19:31Z |
| format | Article |
| id | mit-1721.1/88122 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:19:31Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/881222022-09-30T20:23:23Z Rumors in a Network: Who's the Culprit? Shah, Devavrat Zaman, Tauhid R. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Sloan School of Management Shah, Devavrat Zaman, Tauhid R. We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with the popular susceptible-infected (SI) model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term rumor centrality. We establish that this is a maximum likelihood (ML) estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has nontrivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops of the true source across different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding rumor sources in networks which are not tree-like. United States. Air Force Office of Scientific Research. Complex Networks Program National Science Foundation (U.S.). Division of Human and Social Dynamics National Science Foundation (U.S.). Emerging Models and Technologies for Computation Program MIT-Shell Energy Fellowship 2014-06-30T13:55:48Z 2014-06-30T13:55:48Z 2011-08 2011-02 Article http://purl.org/eprint/type/JournalArticle 0018-9448 1557-9654 http://hdl.handle.net/1721.1/88122 Shah, Devavrat, and Tauhid Zaman. “Rumors in a Network: Who’s the Culprit?” IEEE Trans. Inform. Theory 57, no. 8 (n.d.): 5163–5181. https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0003-4973-9343 en_US http://dx.doi.org/10.1109/TIT.2011.2158885 IEEE Transactions on Information Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) Other univ. web domain |
| spellingShingle | Shah, Devavrat Zaman, Tauhid R. Rumors in a Network: Who's the Culprit? |
| title | Rumors in a Network: Who's the Culprit? |
| title_full | Rumors in a Network: Who's the Culprit? |
| title_fullStr | Rumors in a Network: Who's the Culprit? |
| title_full_unstemmed | Rumors in a Network: Who's the Culprit? |
| title_short | Rumors in a Network: Who's the Culprit? |
| title_sort | rumors in a network who s the culprit |
| url | http://hdl.handle.net/1721.1/88122 https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0003-4973-9343 |
| work_keys_str_mv | AT shahdevavrat rumorsinanetworkwhostheculprit AT zamantauhidr rumorsinanetworkwhostheculprit |