Interactive Recommendation (IR) formulates the recommendation as a multi-step decision-making process which can actively utilize the individuals’ feedback in multiple steps and optimize the long-term user benefit of recommendation. Deep Reinforcement Learning (DRL) has witnessed great application in IR for e-commerce. However, user cold-start problem impairs the learning process of the DRL-based recommendation scheme. Moreover, most existing DRL-based recommendations ignore user relationships or only consider the single-hop social relationships, which cannot fully utilize the social network. The fact that those schemes can not capture the multiple-hop social relationships among users in IR will result in a sub-optimal recommendation. To address the above issues, this paper proposes a Social Graph Neural network-based interactive Recommendation scheme (SGNR), which is a multiple-hop social relationships enhanced DRL framework. Within this framework, the multiple-hop social relationships among users are extracted from the social network via the graph neural network which can sufficiently take advantage of the social network to provide more personalized recommendations and effectively alleviate the user cold-start problem. The experimental results on two real-world datasets demonstrate that the proposed SGNR outperforms other state-of-the-art DRL-based methods that fail to consider social relationships or only consider single-hop social relationships.