Neo4j allows you to store the connections between the people via their contacts, so if you want to leverage the network effect in your application it makes sense to look into that.
It all depends on how you want people to search and interact with your app. If treat people as individual records with no connections then MySQL is good enough. Otherwise Neo4j would probably work better.
IF you have the time to a tiny PoC with some realistic data with both and then decide for yourself.