A growing part of Big Data is made of knowledge graphs. Major knowledge graphs such as Wikidata, DBpedia or the Google Knowledge Graph count millions of entities and billions of semantic links. A major challenge is to enable their exploration and querying by end-users. The SPARQL query language is powerful but provides no support for exploration by endusers. Question answering is user-friendly but is limited in expressivity and reliability. Navigation in concept lattices supports exploration but is limited in expressivity and scalability. In this paper, we introduce a new exploration and querying paradigm, Abstract Conceptual Navigation (ACN), that merges querying and navigation in order to reconcile expressivity, usability, and scalability. ACN is founded on Formal Concept Analysis (FCA) by defining the navigation space as a concept lattice. We then instantiate the ACN paradigm to knowledge graphs (Graph-ACN) by relying on Graph-FCA, an extension of FCA to knowledge graphs. We continue by detailing how Graph-ACN can be efficiently implemented on top of SPARQL endpoints, and how its expressivity can be increased in a modular way. Finally, we present a concrete implementation available online, Sparklis, and a few application cases on large knowledge graphs.