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An element may have heterogeneous semantic interpretations in different ontologies. Therefore, understanding the real local meanings of elements is very useful for ontology operations such as querying and reasoning, which are the foundations for many applications including semantic searching, ontology matching, and linked data analysis. However, since different ontologies have different preferences to describe their elements, obtaining the semantic context of an element is an open problem. A semantic subgraph was proposed to capture the real meanings of ontology elements. To extract the semantic subgraphs, a hybrid ontology graph is used to represent the semantic relations between elements. An extracting algorithm based on an electrical circuit model is then used with new conductivity calculation rules to improve the quality of the semantic subgraphs. The evaluation results show that the semantic subgraphs properly capture the local meanings of elements. Ontology matching based on semantic subgraphs also demonstrates that the semantic subgraph is a promising technique for ontology applications.