As a model of concept representation, ontology has widely applied to various disciplines. In this book, we consider some topics on the sparsity and vulnerability of ontology graph and ontology algorithm. First, the Hermite ontology learning algorithm is presented, and two simulation experimental results show that the proposed new technologies have high accuracy and efficiency on ontology similarity measuring and ontology mapping in certain applications. Second, we determine the isolated toughness condition for an ontology graph to be fractional (f, n’)-critical and fractional (f, n’)-critical deleted. Third, the toughness conditions for fractional (f, n’)-critical ontology graph and fractional (f, n’)-critical deleted ontology graph are given. At last, we discuss some open problems.