Attributed graphs have attracted much attention in recent years. Different from conventional graphs, attributed graphs involve two different types of heterogeneous information, i.e., structural information, which represents the links between the nodes, and attribute information on each of the nodes. Clustering on attributed graphs usually requires the fusion of both types of information in order to identify meaningful clusters. However, most of existing works implement the combination of these two types of information in a "global" manner by treating all nodes equally and learning a global weight for the information fusion. To address this issue, this paper proposed a novel weighted K -means algorithm with "local" learning for attributed graph clustering, called adaptive fusion of structural and attribute information (Adapt-SA) and analyzed the convergence property of the algorithm. The key advantage of this model is to automatically balance the structural connections and attribute information of each node to learn a fusion weight, and get densely connected clusters with high attribute semantic similarity. Experimental study of weights on both synthetic and real-world data sets showed that the weights learned by Adapt-SA were reasonable, and they reflected which one of these two types of information was more important to decide the membership of a node. We also compared Adapt-SA with the state-of-the-art algorithms on the real-world networks with varieties of characteristics. The experimental results demonstrated that our method outperformed the other algorithms in partitioning an attributed graph into a community structure or other general structures.