Neo4j is the leading graph database, made by Neo4j Inc., available as a free open-source Community edition plus a paid Enterprise tier. It ranks #23 in real-world usage at roughly 2.6% adoption, and it's picked whenever the data itself is fundamentally about connections β stored as nodes and relationships instead of rows and tables.
Neo4j's query language, Cypher, reads like an ASCII drawing of the graph pattern you're searching for.
MATCH (p:Person)-[:FRIENDS_WITH]->(f:Person)
WHERE p.name = 'Ada'
RETURN f.name AS friend_name; // finds everyone Ada is friends with
Neo4j Desktop and Neo4j Aura (a free-tier cloud instance) are the two easiest ways to start, both with a browser-based query console and cypher-shell for the command line.
# run locally with Docker
docker run -p 7474:7474 -p 7687:7687 neo4j:latest
# or connect to a running instance with cypher-shell
cypher-shell -u neo4j -p password