Which engine to choose to create your social network?

Question

Social media

The task is to create a social network, the functionality of which can be easily and flexibly customized. We definitely need custom options for fields in the profile, and also, which is also very important, custom types of social connections, moreover, complex ones and with the possibility of some analytics (for example, show all connections of the "friend" type that have more than two "counterparty" type connections). In fact, we need a tool for modeling an arbitrary social system.