A Thorough Comparison Between Independent Cascade and Susceptible-Infected-Recovered Models

2024-08-21

arXiv.org

AI Summary

This paper investigates the disparity in spreading capability between the Independent Cascade (IC) and SIR epidemic models in social networks, and its implications for Influence Maximization (IM). The SIR model’s node recovery mechanism introduces edge-event dependencies that attenuate overall spread. Method: Leveraging coupling arguments, we rigorously prove that, under identical infection parameters, the expected spread size of IC is always at least as large as that of SIR—and the gap can be substantial. Building on this insight, we adapt the Reverse Reachable Set (RR-set) framework to the SIR model and design a scalable, theoretically grounded IM algorithm. Contribution/Results: Our algorithm achieves a $(1-1/e-varepsilon)$ approximation guarantee for SIR-based IM. Experiments on real-world networks demonstrate significant seed-set divergence between IC and SIR due to their structural differences, and validate both the efficacy and practicality of our approach.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the IC model with the node recovery feature. In the SIR model, by computing the probability that a node successfully infects another before its recovery and viewing this probability as the corresponding IC parameter, the SIR model becomes an"out-going-edge-correlated"version of the IC model: the events of the infections along different out-going edges of a node become dependent in the SIR model, whereas these events are independent in the IC model. In this paper, we thoroughly compare the two models and examine the effect of this extra dependency in the SIR model. By a carefully designed coupling argument, we show that the seeds in the IC model have a stronger influence spread than their counterparts in the SIR model, and sometimes it can be significantly stronger. Specifically, we prove that, given the same network, the same seed sets, and the parameters of the two models being set based on the above-mentioned equivalence, the expected number of infected nodes at the end of the cascade for the IC model is weakly larger than that for the SIR model, and there are instances where this dominance is significant. We also study the influence maximization problem with the SIR model. We show that the above-mentioned difference in the two models yields different seed-selection strategies, which motivates the design of influence maximization algorithms specifically for the SIR model. We design efficient approximation algorithms with theoretical guarantees by adapting the reverse-reachable-set-based algorithms, commonly used for the IC model, to the SIR model. Finally, we conduct experimental studies over real-world datasets.

Problem

• Compare IC and SIR models in social networks.
• Analyze dependency effects in SIR model.
• Develop influence maximization algorithms for SIR.

Innovation

• Compares IC and SIR models in social networks
• Adapts reverse-reachable-set algorithms for SIR model
• Proves IC model's stronger influence spread than SIR