  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.
