Realistic modelling of information spread using peer-to-peer diffusion patterns


In computational social science, epidemic-inspired spread models have been widely used to simulate information diffusion. However, recent empirical studies suggest that simple epidemic-like models typically fail to generate the structure of real-world diffusion trees. Such discrepancy calls for a better understanding of how information spreads from person to person in real-world social networks. Here, we analyse comprehensive diffusion records and associated social networks in three distinct online social platforms. We find that the diffusion probability along a social tie follows a power-law relationship with the numbers of disseminator’s followers and receiver’s followees. To develop a more realistic model of information diffusion, we incorporate this finding together with a heterogeneous response time into a cascade model. After adjusting for observational bias, the proposed model reproduces key structural features of real-world diffusion trees across the three platforms. Our finding provides a practical approach to designing more realistic generative models of information diffusion.

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Fig. 1: The unadjusted diffusion probability \({\it{\Lambda }}_{{\it{k}}_{\it{d}},{\it{k}}_{\it{r}}}\) following (kd,kr) links.
Fig. 2: The power-law relationship between peer-to-peer diffusion probability and users’ degrees.
Fig. 3: The power-law distributions of response time τ.
Fig. 4: Comparison of distributions of diffusion tree size N, depth L and structural virality D.
Fig. 5: Distributions of the lifetime T of diffusion trees.
Fig. 6: A consistency check for the observational bias correction using LiveJournal data.

Data availability

Weibo and Twitter data are publicly available at (in Mandarin) and LiveJournal data are subject to restrictions for user privacy protection. Interested readers should contact L. Muchnik ( to gain access to the LiveJournal dataset.

Code availability

Custom code that supports the findings of this study is available at


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B.Z. is funded by Natural Science Foundation of China (grant no. 61503159) and Jiangsu University Overseas Training Programme. S.P. is supported by NIH NIGMS grant no. 5U01GM110748. L.M. is supported by Israel Science Foundation grant no. 1777/17. X.M. and H.E.S. are supported by NSF Grant PHY-1505000 and DTRA grant no. HDTRA-1-14-1-0017. X.X. is supported by National Natural Science Foundation of China (grant no. 61773091). A.S. wishes to thank the Ariel Cyber Innovation Centre in conjunction with the Israel National directorate in the Prime Minister’s Office for their support. S.H. thanks the Italian Ministry of Foreign Affairs and International Cooperation jointly with the Israeli Ministry of Science, Technology, and Space (MOST); the Israel Science Foundation, ONR, the Japan Science Foundation with MOST, BSF-NSF, ARO, the Bar-Ilan University Centre for Research in Applied Cryptography and Cyber Security and DTRA (grant no. HDTRA-1-19-1-0016) for financial support. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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All authors designed the research. B.Z. and S.P. performed the experiments and analysis. B.Z., S.P. and L.M. curated data. B.Z., S.P. and L.M. wrote the first draft of the manuscript. X.M., X.X., A.S., S.H. and H.E.S. reviewed and edited the manuscript.

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Correspondence to Bin Zhou or Sen Pei.

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Zhou, B., Pei, S., Muchnik, L. et al. Realistic modelling of information spread using peer-to-peer diffusion patterns. Nat Hum Behav 4, 1198–1207 (2020).

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