Representation learning is a central problem of attributed networks (ANs) data analysis in a variety of fields. Given an attributed graph, the objectives are to obtain a representation of nodes and a partition of the set of nodes. Usually, these two objectives are pursued separately via two tasks that are performed sequentially, and any benefit that may be obtained by performing them simultaneously is lost. In this brief, we propose a power-attributed graph embedding and clustering (PAGEC for short) in which the two tasks, embedding and clustering, are considered together. To jointly encode data affinity between node links and attributes, we use a new powered proximity matrix. We formulate a new matrix decomposition model to obtain node representation and node clustering simultaneously. Theoretical analysis shows the close connections between the new proximity matrix and the random walk theory on a graph. Experimental results demonstrate that the PAGEC algorithm performs better, in terms of clustering and embedding, than state-of-the-art algorithms including deep learning methods designed for similar tasks in relation to attributed network datasets with different characteristics.