Abstract
Finding information source in viral spreading has important applications such as to root out the culprit of a rumor spreading in online social networks. In particular, given a snapshot observation of the rumor graph, how to accurately identify the initial source of the spreading? In the seminal work by Shah and Zaman in 2011, this statistical inference problem was formulated as a maximum likelihood estimation problem and solved using a rumor centrality approach for graphs that are degree-regular. This however is optimal only if there are no boundary effects, e.g., the underlying number of susceptible vertices is countably infinite. In general, all practical real-world networks are finite or exhibit complex spreading behavior, and therefore these boundary effects cannot be ignored. In this paper, we solve the constrained maximum likelihood estimation problem by a generalized rumor centrality for spreading in graphs with boundary effects. We derive a graph-theoretic characterization of the maximum likelihood estimator for degree-regular graphs with a single end vertex at its boundary and propose a message-passing algorithm that is near-optimal for graphs with more complex boundary consisting of multiple end vertices.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
D. Shah, T. Zaman, Rumors in a network: who’s the culprit? IEEE Trans. Inf. Theory 57, 5163–5181 (2011)
D. Shah, T. Zaman, Rumor centrality: a universal source detector, in Proceedings of ACM SIGMETRICS (2012)
L. Vassio, F. Fagnani, P. Frasca, A. Ozdaglar, Message passing optimization of harmonic influence centrality. IEEE Trans. Control Netw. Syst. 1(1), 109–120 (2014)
N. Karamchandani, M. Franceschetti, Rumor source detection under probabilistic sampling, in Proceedings of IEEE ISIT (2013)
W. Dong, W. Zhang, C.W. Tan, Rooting out the rumor culprit from suspects, in Proceedings of IEEE ISIT (2013)
W. Luo, W.P. Tay, M. Leng, Identifying infection sources and regions in large networks. IEEE Trans. Signal Process. 61(11), 2850–2865 (2013)
Z. Wang, W. Dong, W. Zhang, C.W. Tan, Rumor source detection with multiple observations: fundamental limits and algorithms, in Proceedings of ACM SIGMETRICS (2014)
C.W. Tan, P.D. Yu, C.K. Lai, W. Zhang, H.L. Fu, Optimal detection of influential spreaders in online social networks, in Proceedings of CISS (2016), pp. 145–150
J. Khim, P. Loh, Confidence sets for the source of a diffusion in regular trees. IEEE Trans. Netw. Sci. Eng. 4(1), 27–40 (2017)
N.T.J. Bailey, The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. (Griffin, New York, 1975)
B. Zelinka, Medians and peripherians of trees. Arch. Math. 4(2), 87–95 (1968)
D.J.C. Mackay, Information Theory, Inference and Learning Algorithms, 1st edn. (Cambridge University Press, Cambridge, 2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Yu, PD., Tan, C.W., Fu, HL. (2019). Rumor Source Detection in Finite Graphs with Boundary Effects by Message-Passing Algorithms. In: Kaya, M., Alhajj, R. (eds) Influence and Behavior Analysis in Social Networks and Social Media. ASONAM 2018. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-030-02592-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-02592-2_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-02591-5
Online ISBN: 978-3-030-02592-2
eBook Packages: Social SciencesSocial Sciences (R0)