The social graphs synthesized by the generative models are increasingly in demand due to data scarcity and concerns over user privacy. One of the key performance criteria for generating social networks is the fidelity to specified conditionals, such as users with certain membership and financial status. While recent diffusion models have shown remarkable performance in generating images, their effectiveness in synthesizing graphs has not yet been explored in the context of conditional social graphs. In this paper, we propose the first kind of conditional diffusion model for social networks, CDGraph, which trains and synthesizes graphs based on two specified conditions. We propose the co-evolution dependency in the denoising process of CDGraph to capture the mutual dependencies between the dual conditions and further incorporate social homophily and social contagion to preserve the connectivity between nodes while satisfying the specified conditions. Moreover, we introduce a novel classifier loss, which guides the training of the diffusion process through the mutual dependency of dual conditions. We evaluate CDGraph against four existing graph generative methods, i.e., SPECTRE, GSM, EDGE, and DiGress, on four datasets. Our results show that the generated graphs from CDGraph achieve much higher dual-conditional validity and lower discrepancy in various social network metrics than the baselines, thus demonstrating its proficiency in generating dual-conditional social graphs.

翻译：由于数据稀缺性和用户隐私问题，生成模型合成的社交图需求日益增长。社交网络生成的关键性能指标之一是对指定条件（如具有特定成员身份和财务状况的用户）的忠实度。尽管近年来的扩散模型在图像生成领域展现出卓越性能，但其在条件社交图合成场景下的有效性尚未被探索。本文首次提出面向社交网络的条件扩散模型CDGraph，该模型基于两种指定条件训练并合成社交图。我们在CDGraph的去噪过程中提出共演化依赖机制，以捕获双条件之间的相互依赖关系，并进一步整合社会同质性与社会传染性，在满足指定条件的同时保持节点间的连通性。此外，我们引入一种新型分类器损失函数，通过双条件间的相互依赖引导扩散过程的训练。我们在四个数据集上将CDGraph与四种现有图生成方法（即SPECTRE、GSM、EDGE和DiGress）进行对比评估。结果表明，与基线方法相比，CDGraph生成的图在双条件有效性和多种社交网络度量指标的一致性方面均表现更优，从而证明了其在生成双条件社交图方面的能力。