Recent research studies on social recommendation have focused on the joint modeling of the explicit and implicit relations in social networks and overlooked the special phenomenon that high-order implicit relations are not equally important to each user. The importance of high-order implicit relations to users with plenty of neighbors differs greatly from that to users with few neighbors. In addition, due to the randomness of social relation construction, explicit relations are not always available. This study proposes a novel adaptive high-order implicit relations modeling (AHIRM) method, and the model consists of three components. Specifically, unreliable relations are filtered, and potential reliable relations are identified, thereby mitigating the adverse effects of unreliable relations and alleviating the data sparsity issue. Then, an adaptive random walk algorithm is designed to capture neighbors at different orders for users according to normalized node centrality, construct high-order implicit relations among the users, and ultimately reconstruct the social network. Finally, the graph convolutional network (GCN) is employed to aggregate information about neighbor nodes. User embeddings are thereby updated to model the high-order implicit relations and further alleviate the data sparsity issue. The influence of social structure and personal preference are both considered during modeling, and the process of social influence propagation is simulated and retained. Comparative verification of the proposed model and the existing algorithms are conducted on the LastFM, Douban, and Gowalla datasets, and the results verify the effectiveness and rationality of the proposed AHIRM model.