Social Network: How to map the cypher hop degree to that of the connection degree in a social network

In fig1, I would like to retrieve all the 3rd level connections for person "A" using the query
match (p:Person {name: "A"})-[:FRIENDS_WITH*3]->(p2:Person) return p2
and the output returned is none, which is correct.
But, when I execute the same query for the graph in fig2, the output is person "E", since "B" and "C" are connected now. How do I prevent "E" from being returned as a 3rd level connection?