Redundant relations refer to explicit relations which can also be deducted implicitly. Although there exist several ontology redundancy elimination methods, they all do not take equivalent relations into consideration. Actually, real ontologies usually contain equivalent relations; their redundancies cannot be completely detected by existing algorithms. Aiming at solving this problem, this paper proposes a super-node based ontology redundancy elimination algorithm. The algorithm consists of super-node transformation and transitive redundancy elimination. During the super-node transformation process, nodes equivalent to each other are transferred into a super-node. Then by deleting the overlapped edges, redundancies relating to equivalent relations are eliminated. During the transitive redundancy elimination process, redundant relations are eliminated by comparing concept nodes' direct and indirect neighbors. Most notably, we proposed a theorem to validate real ontology's irredundancy. Our algorithm outperforms others on both real ontologies and synthetic dynamic ontologies.

As the superstructure of knowledge graph, ontology has been widely applied in knowledge engineering. However, it becomes increasingly difficult to be practiced and comprehended due to the growing data size and complexity of schemas. Hence, ontology summarization surfaced to enhance the comprehension and application of ontology. Existing summarization methods mainly focus on ontology's topology without taking semantic information into consideration, while human understand information based on semantics. Thus, we proposed a novel algorithm to integrate semantic information and topological information, which enables ontology to be more understandable. In our work, semantic and topological information are represented by concept vectors, a set of high-dimensional vectors. Distances between concept vectors represent concepts' similarity and we selected important concepts following these two criteria: 1) the distances from important concepts to normal concepts should be as short as possible, which indicates that important concepts could summarize normal concepts well; 2) the distances from an important concept to the others should be as long as possible which ensures that important concepts are not similar to each other. K-means++ is adopted to select important concepts. Lastly, we performed extensive evaluations to compare our algorithm with existing ones. The evaluations prove that our approach performs better than the others in most of the cases.