Knowledge graphs are useful and flexible knowledge representation structures that can facilitate the integration of information in NLP tasks. They are however incomplete, and not only that, but also skewed in the type of knowledge they include. In this talk I will present an investigation into two existing knowledge graphs – Freebase15k and WordNet18 – and show how particular characteristics influence the quality of knowledge graph embeddings, which ultimately impact knowledge graph completion and other tasks. I will also talk about knowledge discovery in knowledge graphs – as paths associated with direct relations – and how these patterns can be used for both "internal" knowledge graph completion and targeted information extraction from external textual sources.