neo4j is described as 'You can think of Neo4j as a high-performance graph engine with all the features of a mature and robust database'. There are more than 10 alternatives to neo4j for a variety of platforms, including Linux, Mac, Windows, Self-Hosted solutions and Online / Web-based. The best alternative is Wikibase, which is both free and Open Source. Other great apps like neo4j are GraphStack.io (Free, Open Source), ArangoDB (Free, Open Source), Titan Database (Free, Open Source) and RedisGraph (Free, Open Source).
Wikibase is the software that runs Wikidata, but is also usable for other projects beyond that. Wikibase allows the collaborative editing of structured data on top of MediaWiki. It is optimized for graph-like, schema-poor data, not for tabular and strongly pre-structured data.
RedisGraph is a property graph database module for Redis. It is the first graph database to use linear algebra on sparse adjacency matrices to implement graph operations, which lets it achieve high performance. It understands OpenCypher queries.