The sets of possible heads and tails for relations in a Knowledge Graph and a type taxonomy of participating entities are important aspects of a Knowledge Graph and constitute a large portion of a Knowledge Graph’s ontology. Making the ontology explicit helps to ensure consistency of the knowledge represented in the graph and allows for less costly maintenance and update of graph content. However, Knowledge Graphs are often conveniently formed without an explicitly described ontology, using only (head, relation, tail)-tuples. For such graphs without predefined structure, we propose learning an ontology and a hierarchical type taxonomy from the graph itself, taking advantage of the reciprocity of entity types and sets of possible heads (relational domains) and tails (relational ranges). Experiments on real-world datasets validate our approach and demonstrate the promise for leveraging machine learning methodologies to efficiently generate taxonomies and ontologies jointly for Knowledge Graphs (Our implementation can be found at https://tinyurl.com/5n6sw6yj).