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Finding Rumor Sources on Random Trees

Author

Listed:
  • Devavrat Shah

    (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Tauhid Zaman

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to when these nodes became infected. In a recent work ( Shah and Zaman 2010 ), this rumor source detection problem was introduced and studied. The authors proposed the graph score function rumor centrality as an estimator for detecting the source. They establish it to be the maximum likelihood estimator with respect to the popular Susceptible Infected (SI) model with exponential spreading times for regular trees. They showed that as the size of the infected graph increases, for a path graph (2-regular tree), the probability of source detection goes to 0 and for d -regular trees with d ≥ 3 the probability of detection, say α d , remains bounded away from 0 and is less than 1/2. However, their results stop short of providing insights for the performance of the rumor centrality estimator in more general settings such as irregular trees or the SI model with nonexponential spreading times.This paper overcomes this limitation and establishes the effectiveness of rumor centrality for source detection for generic random trees and the SI model with a generic spreading time distribution. The key result is an interesting connection between a continuous time branching process and the effectiveness of rumor centrality. Through this, it is possible to quantify the detection probability precisely. As a consequence, we recover all previous results as a special case and obtain a variety of novel results including the universality of rumor centrality in the context of tree-like graphs and the SI model with a generic spreading time distribution.

Suggested Citation

  • Devavrat Shah & Tauhid Zaman, 2016. "Finding Rumor Sources on Random Trees," Operations Research, INFORMS, vol. 64(3), pages 736-755, June.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:3:p:736-755
    DOI: 10.1287/opre.2015.1455
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    References listed on IDEAS

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    1. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
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    Cited by:

    1. Jiang, Meiling & Gao, Qingwu & Zhuang, Jun, 2021. "Reciprocal spreading and debunking processes of online misinformation: A new rumor spreading–debunking model with a case study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Michel Grabisch & Agnieszka Rusinowska & Xavier Venel, 2019. "Diffusion in countably infinite networks," Documents de travail du Centre d'Economie de la Sorbonne 19017, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Edward Anderson & David Gamarnik & Anton Kleywegt & Asuman Ozdaglar, 2016. "Preface to the Special Issue on Information and Decisions in Social and Economic Networks," Operations Research, INFORMS, vol. 64(3), pages 561-563, June.
    4. Shi, Chaoyi & Zhang, Qi & Chu, Tianguang, 2022. "Source estimation in continuous-time diffusion networks via incomplete observation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    5. Sahand Negahban & Sewoong Oh & Devavrat Shah, 2017. "Rank Centrality: Ranking from Pairwise Comparisons," Operations Research, INFORMS, vol. 65(1), pages 266-287, February.
    6. Vahideh Manshadi & Sidhant Misra & Scott Rodilitz, 2020. "Diffusion in Random Networks: Impact of Degree Distribution," Operations Research, INFORMS, vol. 68(6), pages 1722-1741, November.
    7. Gong, Chang & Li, Jichao & Qian, Liwei & Li, Siwei & Yang, Zhiwei & Yang, Kewei, 2024. "HMSL: Source localization based on higher-order Markov propagation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Suisheng Yu & Mingcai Li & Fengming Liu, 2017. "Rumor Identification with Maximum Entropy in MicroNet," Complexity, Hindawi, vol. 2017, pages 1-8, September.
    9. Sahand Negahban & Sewoong Oh & Devavrat Shah, 2017. "Rank Centrality: Ranking from Pairwise Comparisons," Operations Research, INFORMS, vol. 65(1), pages 266-287, February.
    10. Harry Crane & Min Xu, 2021. "Inference on the history of a randomly growing tree," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 639-668, September.

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