A Prior-based Discrete Diffusion Model for Social Graph Generation

Graph generation is essential in social network analysis, particularly for modeling information flow and user interactions. However, existing probabilistic diffusion models face challenges when applied to social propagation graphs. The continuous noise does not apply to the discrete nature of graph generation tasks, and the random Gaussian initialization in the reverse process can introduce biases that deviate from real-world propagation patterns. To address these issues, this paper introduces a Prior-based Discrete Diffusion Model (PDDM) for social graph generation. PDDM redefines the forward process as a discrete process for node denoising and edge generation, and the task of the denoising module is transformed into the connection probability learning of node-level tasks. Further, PDDM employs a new starting point of the reverse process by incorporating user similarity as the probability matrix, which can better leverage the social context. These developments mitigate reverse-starting bias and enhance model robustness. Moreover, PDDM integrates lightweight deep graph networks such as GAT, demonstrating both scalability and applicability to graph generation scenarios. Comprehensive experiments on real-world social network datasets demonstrate PDDM's superiority in terms of the MMD metric and downstream tasks. The code is available at https://github.com/cgao-comp/PDDM.