Open-source graph databases like Memgraph and Neo4j offer both community and enterprise editions, each catering to different needs and budgets. Memgraph, an in-memory graph database, provides robust performance and features such as replication and property constraints in its community edition, making it suitable for small businesses seeking high availability and performance without cost. Neo4j, an on-disk database, offers a rich legacy but limits some features like replication, fast query execution, and property constraints to its enterprise edition, potentially increasing costs due to higher memory usage in production environments. Both databases support graph algorithms through Memgraph's Advanced Graph Extensions (MAGE) and Neo4j's Graph Data Science library (GDS), although Neo4j imposes CPU restrictions in its community edition. Choosing between these databases involves considering not only the available features and performance but also the total cost of ownership, including hosting expenses and additional resources required for optimal performance.