There was a problem where I had to find a list of all my first degree friends who could introduce me to my second degree friends in a Facebook-like graph network. To solve this, I used Cypher queries in Neo4j to retrieve the required information. The query matched nodes and relationships between them, returning a list of names that could act as intermediaries. Additionally, there was another problem where newly added nodes needed to be automatically indexed during batch imports. A workaround was found by creating a new node with an indexable property and then querying it, which effectively indexed the new node in the process.