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Social network information has been widely applied to traditional recommendations that
have received significant attention in recent years. Most existing social recommendation models
tend to use pairwise relationships to explore potential user preferences, but overlook the complexity
of real-life interactions between users and the fact that user relationships may be higher order.
These approaches also ignore the dynamic nature of friend influence, which leads the models to
treat different friend influences equally in different ways. To address this, we propose a social
recommendation algorithm that incorporates graph embedding and higher-order mutual information
maximization based on the consideration of social consistency. Specifically, we use the graph attention
model to build higher-order information among users for deeper mining of their behavioral patterns
on the one hand; while on the other hand, it models user embedding based on the principle of social
consistency to finally achieve finer-grained inference of user interests. In addition, to alleviate the
problem of losing its own hierarchical information after fusing different levels of hypergraphs, we
use self-supervised learning to construct auxiliary branches that fully enhance the rich information in
the hypergraph. Experimental results conducted on two publicly available datasets show that the
proposed model outperforms state-of-the-art methods.