Uncertain graphs, a form of uncertain data, have recently attracted a lot of attention as they can represent inherent uncertainty in collected data. The uncertain graphs pose challenges to conventional data processing techniques and open new research directions. Going in the reserve direction, this paper focuses on the problem of anonymizing a deterministic graph by converting it into an uncertain form. The paper first analyzes drawbacks in a recent uncertainty-based anonymization scheme and then proposes Maximum Variance, a novel approach that provides better tradeoff between privacy and utility. Towards a fair com-parison between the anonymization schemes on graphs, the second con-tribution of this paper is to describe a quantifying framework for graph anonymization by assessing privacy and utility scores of typical schemes in a unified space. The extensive experiments show the effectiveness and efficiency of Maximum Variance on three large real graphs.