Abstract
Information cascades on social networks, such as retweet cascades on Twitter, have been often viewed as an epidemiological process, with the associated notion of virality to capture popular cascades that spread across the network. The notion of structural virality (or average path length) has been posited as a measure of global spread.
In this paper, we argue that this simple epidemiological view, though analytically compelling, is not the entire story. We first show empirically that the classical SIR diffusion process on the Twitter graph, even with the best possible distribution of infectiousness parameter, cannot explain the nature of observed retweet cascades on Twitter. More specifically, rather than spreading further from the source as the SIR model would predict, many cascades that have several retweets from direct followers, die out quickly beyond that.
We show that our empirical observations can be reconciled if we take interests of users and tweets into account. In particular, we consider a model where users have multi-dimensional interests, and connect to other users based on similarity in interests. Tweets are correspondingly labeled with interests, and propagate only in the subgraph of interested users via the SIR process. In this model, interests can be either narrow or broad, with the narrowest interest corresponding to a star graph on the interested users, with the root being the source of the tweet, and the broadest interest spanning the whole graph. We show that if tweets are generated using such a mix of interests, coupled with a varying infectiousness parameter, then we can qualitatively explain our observation that cascades die out much more quickly than is predicted by the SIR model. In the same breath, this model also explains how cascades can have large size, but low “structural virality” or average path length.
H. Zhang—This work was partly done when the author was an intern at Twitter, Inc.
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Notes
- 1.
Indeed, the median of first level impressions is 175, while the median of second level impressions is 29!
- 2.
A lot of spam tweets have star-like cascade structure that may significantly impact the experiment results while not representing general user behavior.
- 3.
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Acknowledgment
We are grateful to the anonymous reviewers for very helpful feedbacks. Goel and Zhang are supported by DARPA GRAPHS program via grant FA9550-12-1-0411. Munagala is supported in part by NSF grants CCF-1348696, CCF-1408784, and IIS-1447554, and by grant W911NF-14-1-0366 from the Army Research Office (ARO).
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Goel, A., Munagala, K., Sharma, A., Zhang, H. (2015). A Note on Modeling Retweet Cascades on Twitter. In: Gleich, D., Komjáthy, J., Litvak, N. (eds) Algorithms and Models for the Web Graph. WAW 2015. Lecture Notes in Computer Science(), vol 9479. Springer, Cham. https://doi.org/10.1007/978-3-319-26784-5_10
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