Graph models and algorithms are ubiquitous, due to their suitability for knowledge representation in e-commerce, social media networks, research, computer networks, electronics, as well as for maximum flow problems, route problems, and web searches. Graph databases are databases with Create, Read, Update, and Delete (CRUD) methods exposing a graph data model, such as property graphs (containing nodes and relationships), hypergraphs (a relationship can connect any number of nodes), RDF triples (subject-predicate-object), or quads (named graph-subject-predicate-object). Graph databases are usually designed for online transactional processing (OLTP) systems and optimized for transactional performance, integrity, and availability. Unlike relational and NoSQL databases, purpose-build graph databases, including triplestores and quadstores, do not rely on indices, because graphs naturally provide an adjacency index, and relationships attached to a node provide a direct connection to other related nodes. Graph queries are performed using this locality to traverse through the graph, which can be carried out with several orders of magnitude higher efficiency than that of relational databases joining data through a global index. In fact, most graph databases are so powerful that they are suitable even for Big Data applications.