  Social relations have been widely incorporated into recommender systems to
alleviate data sparsity problem. However, raw social relations don't always
benefit recommendation due to their inferior quality and insufficient quantity,
especially for inactive users, whose interacted items are limited. In this
paper, we propose a novel social recommendation method called LSIR
(\textbf{L}earning \textbf{S}ocial Graph for \textbf{I}nactive User
\textbf{R}ecommendation) that learns an optimal social graph structure for
social recommendation, especially for inactive users. LSIR recursively
aggregates user and item embeddings to collaboratively encode item and user
features. Then, graph structure learning (GSL) is employed to refine the raw
user-user social graph, by removing noisy edges and adding new edges based on
the enhanced embeddings. Meanwhile, mimic learning is implemented to guide
active users in mimicking inactive users during model training, which improves
the construction of new edges for inactive users. Extensive experiments on
real-world datasets demonstrate that LSIR achieves significant improvements of
up to 129.58\% on NDCG in inactive user recommendation. Our code is available
at~\url{https://github.com/liun-online/LSIR}.
