We address the question why among the multitude of imaginable CnHm compositions some are easily synthesizable and abundant in nature, while others are not. To shed light on this problem we borrow approaches from nanocluster study, where stability with respect to neighboring compositions is used as a criterion of "magic" (particularly stable) clusters. By merging this criterion with predictions of lowest-energy structures of all CnHm molecules in a wide range of compositions (n ≤ 20, m ≤ 42) we provide guidelines for predicting the presence or absence of certain hydrocarbon molecules in various environments, their relative abundance and reactivity/inertness. The resulting maps of stability show the increased stability of C2nH2 compounds, polyaromatic hydrocarbons, and diamondoids, which is supported by experimental studies of the interstellar medium, flames, and petroleum fractions. This approach can be applied to any other molecular system, rationalizing the diversity of known compounds and predicting new potentially synthesizable molecules.