Source-linked AI summary
Information Diffusion and External Influence in Networks
Seth A. Myers, Chenguang Zhu, Jure Leskovec
TL;DR
Information diffusion can reflect both social-network transmission and external out-of-network exposure, but these sources are difficult to disentangle. The paper develops a probabilistic model and efficient fitting method to separate them in Twitter data, finding that 71% of URL mentions are attributable to network effects and 29% to external sources.
Problem
Existing network-adoption models largely treat information as passing along edges, leaving social and external influences confounded when both can expose a node.
Method
The paper models internal and external exposures separately, infers an event profile and exposure curve, and fits them iteratively from network and infection-time data.
Results
71% of Twitter URL mentions are attributed to network effects and 29% to external out-of-network sources; the inferred exposure curve is often 50% more accurate than baselines.
Takeaways & Limitations
Information in Twitter often jumps across the network, and external sources account for a substantial share of observed URL diffusion.
Takeaways & Limitations
The baseline external-activity scale is usually 1 to 2 orders of magnitude larger because infection counts alone identify the event-profile shape, not its scale, without the exposure curve.
Abstract
from arXiv · showhide
Social networks play a fundamental role in the diffusion of information. However, there are two different ways of how information reaches a person in a network. Information reaches us through connections in our social networks, as well as through the influence of external out-of-network sources, like the mainstream media. While most present models of information adoption in networks assume information only passes from a node to node via the edges of the underlying network, the recent availability of massive online social media data allows us to study this process in more detail. We present a model in which information can reach a node via the links of the social network or through the influence of external sources. We then develop an efficient model parameter fitting technique and apply the model to the emergence of URL mentions in the Twitter network. Using a complete one month trace of Twitter we study how information reaches the nodes of the network. We quantify the external influences over time and describe how these influences affect the information adoption. We discover that the information tends to "jump" across the network, which can only be explained as an effect of an unobservable external influence on the network. We find that only about 71% of the information volume in Twitter can be attributed to network diffusion, and the remaining 29% is due to external events and factors outside the network.
1. INTRODUCTION
Information can reach network nodes through social ties or external sources, but these pathways are confounded when both are possible. The paper models and separates them using Twitter data, finding substantial external influence on URL diffusion.
- Motivation: Massive online social-media data make it possible to study mass-media effects and network influence simultaneously in finer detail.The paper analyzes over 3 billion tweets from a complete one-month Twitter trace.
- Motivation: The paper contrasts diffusion over network edges with external influence, where information can “jump” across the network.An appearance at a node without previously mentioning neighbors can only be explained by an unobserved exogenous source.
- Model: The model is a probabilistic generative account in which information reaches nodes through social-network links or external sources.It is designed to separate the two factors despite their confounding.
- Model: The model distinguishes internal exposures from external exposures and uses an exposure curve to map repeated exposures to infection probability.External exposure volume over time is represented by the event profile.
- Findings: 71% of URL mentions on Twitter can be attributed to network effects, while the remaining 29% seem due to external out-of-network sources.The analysis fits the model to 18,186 URLs appearing across Twitter users.
- Findings: 50% more accurate than baseline methods is the reported accuracy of the inferred exposure curve in many cases.The model also detects external out-of-network events and analyzes how topics differ in their external and internal drivers.
2. RELATED WORK
Prior work commonly modeled information emergence as diffusion through network edges. External influence had also been studied, but this paper’s approach directly models the network and node-to-node interactions.
- Network diffusion: Diffusion-of-innovations research provides a conceptual framework in which active nodes spread information along network edges.A broad set of models describes mechanisms by which contagions spread from infected nodes.
- External influence: Earlier YouTube work inferred external influence from videos becoming popular faster than a completely connected-network diffusion model predicted.That approach used an implicit completely connected network.
- External influence: This paper differs by directly considering the network and node-to-node interactions while explicitly inferring external influence.Its approach therefore separates network effects from out-of-network effects within the observed network.
3. PROPOSED MODEL
The proposed model treats information adoption as driven by both network-mediated exposures and unobservable external exposures, while distinguishing exposure events from infection decisions. It estimates the time-varying external event profile and exposure-curve parameters from infection times, using an alternating inference strategy and scalable approximations.
- The model incorporates information spread along network edges and external influences, reconciling continuous exposure arrivals with discrete infection decisions.
- An exposure occurs when a node becomes aware of information, whereas an infection occurs when it posts a tweet containing that information.
- The external event profile λext(t) represents the time-varying intensity of unobservable external exposures, which can recur for any node.
- External exposure counts are modeled with a binomial distribution after discretizing time, then approximated for continuous time and varying external intensity.
- The exposure curve η(x) gives infection probability after the xth exposure, with ρ1 measuring peak infectiousness and ρ2 measuring enduring relevancy.
- 3.1 Inferring the model parameters: The fitting procedure alternates between estimating λext(t) and η(x), fixes ρ2 across candidate integer values, and selects the result with optimal log-likelihood.
- 3.1 Inferring the model parameters: The method uses expected counts of uninfected nodes to infer the external profile and converges quickly because terms independent of ρ1 are computed only once.
- 3.1 Inferring the model parameters: Restricting inference to the first M infections makes runtime constant with respect to contagion duration, with only a negligible decrease in accuracy.
Given
The section contrasts observed infections with their predicted infections, including internal and external infection categories.
- Infections are presented alongside predicted infections for comparison.
Inferred by the model
The model infers internal and external contagion dynamics from infection data and remains computationally practical across synthetic and real contagions.
- The model detected four Tucson shooting developments, each followed by an event-profile spike within 10 hours.
- Typical contagions infecting 50-100 nodes converged in under a minute, while larger contagions infecting thousands took 5-10 minutes.
- The algorithm fitted more than 18,000 real contagions and hundreds of synthetic contagions without convergence issues.
4. EXPERIMENTS
Experiments on synthetic and Twitter data show that the model can separate internal diffusion from external influence and recover exposure dynamics. Large-scale URL analysis reveals selective, rapidly fatiguing adoption and substantial external exposure.
- Synthetic-data experiments: Over 100 synthetic-data combinations on networks of 75k+ nodes showed the algorithm performed consistently well and significantly better than baselines.
- Synthetic-data experiments: The inferred event profile closely matched ground truth, while the baseline misplaced its peak and differed by several orders of magnitude in scale.
- Synthetic-data experiments: The model resolved all 10 peaks in a zig-zag external-influence profile, whereas the baseline detected only 4 peaks.
- Real-data experiments: 1.14 was the exponent of the power-law lag-time distribution between infections and exposures in empirical analysis.
- Real-data experiments: Across 1,929 URLs in 11 news categories, the average fraction of external infections was 23.94%, with Politics most externally driven and Entertainment most internally driven.
- Real-data experiments: 71% of exposures came from internal network sources and 29% from external sources, indicating that external effects cannot be ignored.
5. CONCLUSION
The paper concludes that information emergence on Twitter reflects both network diffusion and external influence, with external influence accounting for a substantial share of URL mentions. Relaxing the model’s uniform-external-activity assumption is identified as an important direction for future work.
- Around 71% of URL mentions on Twitter are attributed to network effects, while the remaining 29% seem due to external out-of-network sources.
- The model captures external influence and consequently provides a more accurate description of real network diffusion.
- The model assumes uniform external-source activity across all network nodes, motivating future analyses of heterogeneous and individual-level effects.