Spectral community detection algorithms generally divide the network via structure, which is often limited by the number of divisions and it is difficult to control the degree of overlapping. This paper designs an overlapping multiway spectral community detection algorithm  for attribute network, which can divide the attribute network into any number of overlapping communities and effectively discover outliers. Firstly, the partition mapping method from maximization to node vectorization is designed based on the weighted modularity. Secondly, the initial selection strategy of cluster center vectors is given and merged in the attributed network. Thirdly, the node allocation strategy is designed to calculate the inner product of the node and clustering center vector and to assign the node to the community with the highest inner product. Finally, the tightly structured overlapping communities that have out- liers are effectively detected. In addition, applying the algorithm to multiple networks in the real world verifies the effectiveness and efficiency of the proposed algorithm.