One important task in single-cell analysis is to quantify the differentiation potential of single cells. Though various single-cell potency measures have been proposed, they are based on individual biological sources, thus not robust and reliable. It is still a challenge to combine multiple sources to generate a relatively reliable and robust measure to estimate differentiation. In this paper, we propose a New Centrality measure with Gene ontology information (NCG) to estimate single-cell potency. NCG is designed by combining network topology property with edge clustering coefficient, and gene function information using gene ontology function similarity scores. NCG distinguishes pluripotent cells from non-pluripotent cells with high accuracy, correctly ranks different cell types by their differentiation potency, tracks changes during the differentiation process, and constructs the lineage trajectory from human myoblasts into skeletal muscle cells. These indicate that NCG is a reliable and robust measure to estimate single-cell potency. NCG is anticipated to be a useful tool for identifying novel stem or progenitor cell phenotypes from single-cell RNA-Seq data. The source codes and datasets are available at https://github.com/Xinzhe-Ni/NCG.