Примененные запросы:

MATCH (n)
DETACH DELETE n

UNWIND $props as user 
MERGE(p1:  Participants1 {name: user.fullname1, id_event: user.id_event })
MERGE(p2:  Participants2 {name: user.fullname2, id_event: user.id_event })
MERGE(e: Event {name: user.id_event})

MATCH (n:Participants1) RETURN n LIMIT 100
MATCH (n:Event) RETURN n LIMIT 100
MATCH (n:Participants2) RETURN n LIMIT 100

MATCH (p1:Participants1), (p2:Participants2), (e:Event) 
WHERE p1.id_event = p2.id_event = e.name
CREATE 
(p1)-[:LINK]->(e),
(p2)-[:LINK]->(e)

MATCH p=()-[r:LINK]->() RETURN p LIMIT 100

MATCH (properties: Participants1 | Participants2)
WHERE properties.name = $name
RETURN properties ```

Ссылки на документацию (не все):
https://neo4j.com/docs/cypher-manual
https://neo4j.com/docs/python-manual/current/
https://habr.com/ru/post/650623/
https://www.tutorialspoint.com/neo4j/neo4j_cql_creating_relationship.htm