This question is almost impossible to answer because of the generality. I think you are looking for some sort of easy answer problem = solution. The problem is that each "problem" becomes more and more unique as it becomes a business.
What do you call a social network? Twitter? Facebook? LinkedIn? Stack Overflow? They all use different solutions for different parts, and many solutions can exist that use polyglot approach. Twitter has a graph like concept, but there are only 1 degree connections, followers and following. LinkedIn on the other hand thrives on showing how people are connected beyond first degree. These are two different processing and data needs, but both are "social networks".
If you have a "social network" but don't do any discovery mechanisms, then you can easily use any basic key-value store most likely. If you need high performance, horizontal scale, and will have secondary indexes or full-text search, you could use Couchbase.
If you are doing machine learning on top of the log data you are gathering, you can integrate Hadoop with Hive or Pig, or Spark/Shark. Or you can do a lambda architecture and use many different systems with Storm.
If you are doing discovery via graph like queries that go beyond 2nd degree vertexes and also filter on edge properties you likely will consider graph databases on top of your primary store. However graph databases aren't good choices for session store, or as general purpose stores, so you will need a polyglot solution to be efficient.
What is the data velocity? scale? how do you want to manage it. What are the expertise you have available in the company or startup. There are a number of reasons this is not a simple question and answer.
