Document Open Access Logo

Rumors with Changing Credibility

Authors Charlotte Out , Nicolás Rivera , Thomas Sauerwald , John Sylvester

Thumbnail PDF


  • Filesize: 0.93 MB
  • 23 pages

Document Identifiers

Author Details

Charlotte Out
  • Department of Computer Science & Technology, University of Cambridge, UK
Nicolás Rivera
  • Facultad de Ciencias, Universidad de Valparaíso, Chile
Thomas Sauerwald
  • Department of Computer Science & Technology, University of Cambridge, UK
John Sylvester
  • Department of Computer Science, University of Liverpool, UK

Cite AsGet BibTex

Charlotte Out, Nicolás Rivera, Thomas Sauerwald, and John Sylvester. Rumors with Changing Credibility. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 86:1-86:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Randomized rumor spreading processes diffuse information on an undirected graph and have been widely studied. In this work, we present a generic framework for analyzing a broad class of such processes on regular graphs. Our analysis is protocol-agnostic, as it only requires the expected proportion of newly informed vertices in each round to be bounded, and a natural negative correlation property. This framework allows us to analyze various protocols, including PUSH, PULL, and PUSH-PULL, thereby extending prior research. Unlike previous work, our framework accommodates message failures at any time t ≥ 0 with a probability of 1-q(t), where the credibility q(t) is any function of time. This enables us to model real-world scenarios in which the transmissibility of rumors may fluctuate, as seen in the spread of "fake news" and viruses. Additionally, our framework is sufficiently broad to cover dynamic graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Stochastic processes
  • Rumor spreading
  • epidemic algorithms
  • "fake news"


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Ruben Becker, Arnaud Casteigts, Pierluigi Crescenzi, Bojana Kodric, Malte Renken, Michael Raskin, and Viktor Zamaraev. Giant components in random temporal graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2023, volume 275 of LIPIcs, pages 29:1-29:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL:
  2. Stephen Boyd, Arpita Ghosh, Balaji Prabhakar, and Devavrat Shah. Randomized gossip algorithms. IEEE transactions on information theory, 52(6):2508-2530, 2006. Google Scholar
  3. Andrei Z. Broder, Alan M. Frieze, Stephen Suen, and Eli Upfal. Optimal construction of edge-disjoint paths in random graphs. SIAM J. Comput., 28(2):541-573, 1998. URL:
  4. H. Bruns, F.J. Dessart, and M. Pantazi. Covid-19 misinformation: Preparing for future crises. Technical report, EUR 31139 EN, Publications Office of the European Union, Luxembourg, JRC130111., 2022. Google Scholar
  5. Arnaud Casteigts, Michael Raskin, Malte Renken, and Viktor Zamaraev. Sharp thresholds in random simple temporal graphs. In 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, pages 319-326. IEEE, 2021. URL:
  6. Flavio Chierichetti, George Giakkoupis, Silvio Lattanzi, and Alessandro Panconesi. Rumor spreading and conductance. J. ACM, 65(4), April 2018. URL:
  7. F.K. Chung and L. Lu. Concentration inequalities and martingale inequalities: A survey. Internet Mathematics, 3(1):79-127, 2007. Google Scholar
  8. Andrea Clementi, Riccardo Silvestri, and Luca Trevisan. Information spreading in dynamic graphs. In Proceedings of the 2012 ACM symposium on Principles of distributed computing, pages 37-46, 2012. Google Scholar
  9. Andrea E. F. Clementi, Pierluigi Crescenzi, Carola Doerr, Pierre Fraigniaud, Francesco Pasquale, and Riccardo Silvestri. Rumor spreading in random evolving graphs. Random Struct. Algorithms, 48(2):290-312, 2016. URL:
  10. Rami Daknama, Konstantinos Panagiotou, and Simon Reisser. Robustness of randomized rumour spreading. Combinatorics, Probability and Computing, 30(1):37-78, 2021. URL:
  11. Sebastian Daum, Fabian Kuhn, and Yannic Maus. Rumor spreading with bounded in-degree. Theor. Comput. Sci., 810:43-57, 2020. URL:
  12. Michela Del Vicario, Alessandro Bessi, Fabiana Zollo, Fabio Petroni, Antonio Scala, Guido Caldarelli, H Eugene Stanley, and Walter Quattrociocchi. The spreading of misinformation online. Proceedings of the national academy of Sciences, 113(3):554-559, 2016. Google Scholar
  13. Alan Demers, Dan Greene, Carl Hauser, Wes Irish, John Larson, Scott Shenker, Howard Sturgis, Dan Swinehart, and Doug Terry. Epidemic algorithms for replicated database maintenance. In Proceedings of the sixth annual ACM Symposium on Principles of distributed computing, pages 1-12, 1987. Google Scholar
  14. Benjamin Doerr, Mahmoud Fouz, and Tobias Friedrich. Why rumors spread so quickly in social networks. Communications of the ACM, 55(6):70-75, 2012. Google Scholar
  15. Benjamin Doerr and Anatolii Kostrygin. Randomized rumor spreading revisited. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  16. Nikolaos Fountoulakis, Anna Huber, and Konstantinos Panagiotou. Reliable broadcasting in random networks and the effect of density. In 2010 Proceedings IEEE INFOCOM, pages 1-9. IEEE, 2010. Google Scholar
  17. Nikolaos Fountoulakis and Konstantinos Panagiotou. Rumor spreading on random regular graphs and expanders. Random Struct. Algorithms, 43(2):201-220, 2013. Google Scholar
  18. Alan M Frieze and Geoffrey R Grimmett. The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics, 10(1):57-77, 1985. Google Scholar
  19. George Giakkoupis. Tight bounds for rumor spreading with vertex expansion. In Chandra Chekuri, editor, Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, pages 801-815. SIAM, 2014. URL:
  20. George Giakkoupis, Thomas Sauerwald, and Alexandre Stauffer. Randomized rumor spreading in dynamic graphs. In Automata, Languages, and Programming: 41st International Colloquium, ICALP 2014, Proceedings, Part II 41, pages 495-507. Springer, 2014. Google Scholar
  21. Lee Howell. Digital wildfires in a hyperconnected world. World Economic Forum report, 3(2013):15-94, 2013. Google Scholar
  22. Mark Jerrum and Alistair Sinclair. Approximating the permanent. SIAM journal on computing, 18(6):1149-1178, 1989. Google Scholar
  23. Richard Karp, Christian Schindelhauer, Scott Shenker, and Berthold Vocking. Randomized rumor spreading. In Proceedings 41st Annual Symposium on Foundations of Computer Science, pages 565-574. IEEE, 2000. Google Scholar
  24. David Kempe, Jon Kleinberg, and Éva Tardos. Maximizing the spread of influence through a social network. In Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 137-146, 2003. Google Scholar
  25. William Ogilvy Kermack and Anderson G McKendrick. A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, 115(772):700-721, 1927. Google Scholar
  26. Taichi Murayama, Shoko Wakamiya, Eiji Aramaki, and Ryota Kobayashi. Modeling the spread of fake news on twitter. PLOS ONE, 16(4):1-16, April 2021. URL:
  27. Charlotte Out, Nicolás Rivera, Thomas Sauerwald, and John Sylvester. Rumors with changing credibility, 2023. URL:
  28. Konstantinos Panagiotou, Xavier Perez-Gimenez, Thomas Sauerwald, and He Sun. Randomized rumour spreading: The effect of the network topology. Combinatorics, Probability and Computing, 24(2):457-479, 2015. Google Scholar
  29. Konstantinos Panagiotou, Ali Pourmiri, and Thomas Sauerwald. Faster rumor spreading with multiple calls. Electron. J. Comb., 22(1):1, 2015. URL:
  30. F Peter. `bogus’ AP tweet about explosion at the white house wipes billions off us markets. The Telegraph, 2013. URL:
  31. José R.C. Piqueira, Mauro Zilbovicius, and Cristiane M. Batistela. Daley–kendal models in fake-news scenario. Physica A: Statistical Mechanics and its Applications, 548:123406, 2020. URL:
  32. Boris Pittel. On spreading a rumor. SIAM Journal on Applied Mathematics, 47(1):213-223, 1987. Google Scholar
  33. Ali Pourmiri and Bernard Mans. Tight analysis of asynchronous rumor spreading in dynamic networks. In Proceedings of the 39th Symposium on Principles of Distributed Computing, pages 263-272, 2020. Google Scholar
  34. Amir Sarid. The spectral gap of random regular graphs. arXiv, 2022. URL:
  35. Savvas Zannettou, Michael Sirivianos, Jeremy Blackburn, and Nicolas Kourtellis. The web of false information: Rumors, fake news, hoaxes, clickbait, and various other shenanigans. ACM J. Data Inf. Qual., 11(3):10:1-10:37, 2019. URL:
  36. Ahad N. Zehmakan, Charlotte Out, and Sajjad Hesamipour Khelejan. Why rumors spread fast in social networks, and how to stop it. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI 2023, pages 234-242., 2023. URL:
  37. Laijun Zhao, Wanlin Xie, H Oliver Gao, Xiaoyan Qiu, Xiaoli Wang, and Shuhai Zhang. A rumor spreading model with variable forgetting rate. Physica A: Statistical Mechanics and its Applications, 392(23):6146-6154, 2013. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail