The ability to quantify differentiation potential of single cells is a task of critical importance for single-cell studies. So far however, there is no robust general molecular correlate of differentiation potential at the single cell level. Here we show that differentiation potency of a single cell can be approximated by computing the signaling promiscuity, or entropy, of a cells transcriptomic profile in the context of a cellular interaction network, without the need for model training or feature selection. We validate signaling entropy in over 7,000 single cell RNA-Seq profiles, representing all main differentiation stages, including time-course data. We develop a novel algorithm called Single Cell Entropy (SCENT), which correctly identifies known cell subpopulations of varying potency, enabling reconstruction of cell-lineage trajectories. By comparing bulk to single cell data, SCENT reveals that expression heterogeneity within single cell populations is regulated, pointing towards the importance of cell-cell interactions. In the context of cancer, SCENT can identify drug resistant cancer stem-cell phenotypes, including those obtained from circulating tumor cells. In summary, SCENT can directly estimate the differentiation potency and plasticity of single-cells, allowing unbiased quantification of intercellular heterogeneity, and providing a means to identify normal and cancer stem cell phenotypes.