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：由于数据稀缺和用户隐私问题，生成模型合成的社交图需求日益增长。生成社交网络的关键性能指标之一是对特定条件（如具有特定成员身份和财务状况的用户）的忠实度。尽管近期扩散模型在图像生成领域展现出卓越性能，但其在图合成场景中针对条件社交图的有效性尚未得到探索。本文首次提出面向社交网络的条件扩散模型CDGraph，该模型基于双重指定条件进行训练和图合成。我们在CDGraph的去噪过程中提出协同演化依赖机制，以捕捉双重条件之间的相互依赖关系，并进一步融合社交同质性与社交传染性，在满足指定条件的同时保持节点间的连接性。此外，我们引入一种新颖的分类器损失函数，通过双重条件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（SPECTRE、GSM、EDGE和DiGress）进行对比评估。结果表明，与基线方法相比，CDGraph生成的图在双重条件有效性上显著提升，并在多种社交网络度量指标中呈现更低的偏差，充分验证了其在生成双条件社交图方面的优越性能。