Food pairing has not yet been fully pioneered, despite our everyday experience with food and the large amount of food data available on the web. The complementary food pairings discovered thus far created by the intuition of talented chefs, not by scientific knowledge or statistical learning. We introduce FlavorGraph which is a large-scale food graph by relations extracted from million food recipes and information of 1,561 flavor molecules from food databases. We analyze the chemical and statistical relations of FlavorGraph and apply our graph embedding method to better represent foods in dense vectors. Our graph embedding method is a modification of metapath2vec with an additional chemical property learning layer and quantitatively outperforms other baseline methods in food clustering. Food pairing suggestions made based on the food representations of FlavorGraph help achieve better results than previous works, and the suggestions can also be used to predict relations between compounds and foods. Our research offers a new perspective on not only food pairing techniques but also food science in general.