Anonymization is a practical solution for preserving user's identity privacy before data publishing. There are various anonymity techniques can be applied to maintain data utility of micro-data and social networks, however these methods lead to a high runtime or low anonymous graph utility. In this article, an efficient, utility-preserving approach has been proposed to reduce anonymization runtime as well as the amount of information loss incurred by graph anonymization. We craft our anonymization algorithm by combining greedy partition-based aggregating with multi-dimensional sorting as main heuristic tools. The proposed algorithm generates a partial order of the vertices so that the vertex at top rank and another vertex at bottom rank can never be aggregated in the same group, the runtime is reduced. Greedy partition-based aggregating is employed to create k-anonymous clusters which minimizing information loss. Experimental results on real-world datasets show the proposed method has good performance and is superior to the existing methods.