Entropic causal inference is a recent framework for learningthe causal graph between two variables from observationaldata for structural causal models with small entropy. In thispaper, we first extend the causal graph identifiability resultin the two-variable setting under relaxed assumptions. Next,we show the first identifiability result using the entropic ap-proach for learning causal graphs with more than two nodes.We provide a sequential peeling algorithm that is provably cor-rect for general graphs. We also propose a heuristic algorithmfor small graphs that shows strong empirical performance.We conduct rigorous experiments that demonstrate the perfor-mance of our algorithms compared to the existing work usingsynthetic data with different generative models. Finally wetest our algorithms on real-world datasets.