Independent Cascade with Invitation (ICI) Model for Invitation-Aware Diffusion in Social Networks

Background: Invitation-aware diffusion (IAD) describes how information spreads via invitation mechanisms in private social networks, such as WeChat, LinkedIn, and online games. Existing studies focus on macroscopic properties but lack a generic model that captures invitation behavior.

Related work and challenges: Prior models (Independent Cascade, Linear Threshold) do not account for the multi-stage conversion (invitee → acceptor → new inviter) inherent in IAD, making it difficult to adapt traditional diffusion models to invitation-driven scenarios.

Main contributions: The authors propose the Independent Cascade with Invitation (ICI) model, a generic diffusion model that incorporates invitation behavior using the traditional IC influence process, models user role transitions (Inviter, Invitee, Acceptor) with probability parameters, and validates the design through empirical studies on game-based IAD. The ICI algorithm is also applicable to other conversion-funnel diffusion settings.

ICI propagation model: Users are classified as Inviter, Invitee, or Acceptor. Each Inviter independently attempts to invite friends with a set invitation probability. Invitees may become Acceptors with a given acceptance probability, and Acceptors may become new Inviters with a conversion probability. These probabilities control the multi-stage behavior transition.

Offline experimental results: On real-world datasets (TXG-A–D from Tencent RPG games, and public Diggs and Twitter datasets), ICI outperforms baseline IC and LT models in cascade estimation (up to 5× improvement) and diffusion prediction (up to 40.3% gain in AUC/MAP).

Application 1 – Friend recommendation: Integrating ICI influence scores into a friend‑list recommendation system for a social raffle activity increased invitation rates by 20.3% (August) and 10.8% (September) and payment rates by 31.6% (August) and 3.7% (September) over a closeness‑based baseline.

Application 2 – Seed spread: Using ICI‑based influence maximization to select seed users in a FPS game’s seed‑spread activity yielded a 170% increase in spread increment and a 37.5% lift in left‑end user invitation rate compared with a degree‑centrality baseline.

Conclusion: The ICI model demonstrates strong predictive and optimization capabilities for invitation‑driven diffusion, showing significant gains in game scenarios. Future work will focus on deeper model learning, parameter tuning, and broader social‑network applications.