Abstract: In order to capture the global and local structural changes simultaneously, an outlier detection method based on mutual neighbor degree optimization is proposed. The second-order adjacency between the vertices of the network graph was explicitly maintained to maintain the global structure of the underlying network. For the perpendicularity of a given subgraph generated by random walk, the similarity between their embeddings was increased, so as to maintain the first-order mutual adjacency and the local structure of the network. Further, the clustering coefficient of the subgraph was calculated by the embedding function. The proposed method was evaluated on five datasets. The results show that the method has certain advantages in detection accuracy, scalability and stability.