I read recently a blog post that stipulated that cities are more innovative than rural areas, and that was because of the number of interactions. Therefore, seems the logical conclusion, social media spaces with lots of interaction should be the most innovative. You can see the post here, referencing the book Where Good Ideas Come From. I haven't read the book but I hope the thinking goes a bit deeper than what's on the post.
Yes, good social interactions, whether at a university, or a city, or a social media site, can lead to good ideas, but if that were all that were necessary then Jerusalem or Cairo would be the epicenter of innovation, since they are very old cities with large populations. Clearly, there are major cities where innovation flourishes, like San Francisco or Shanghai, and major cities where innovation doesn't exist or occurs with far less frequency. In fact it would probably be easier to name major cities where innovation was more likely not to occur than to occur. So clearly it's not necessarily about a city, or about the number of interactions that matter.
Orwell demonstrated this in his book 1984. Winston Smith had plenty of interactions and lived in a large city, but ideas were repressed and information limited. There was one dominant party line. Whether we are talking about a city, or a social network, there is more required for good ideas than simply the number of interactions. While a network's value increases by the square of its nodes, from an insight and innovation perspective it increases exponentially on the differences of its engaged nodes. That means that more than interaction - interaction with people who have different experiences, beliefs, knowledge and perspectives drives new ideas. Also, the network cannot remain static - it must change or becomes obsolete very quickly. That's why, increasingly, some cities and some networks are as valuable as others. They aren't as dynamic and vibrant and don't include a broad source of perspectives.
While Facebook and LinkedIn and other social platforms may create many communities and large networks, they don't create heterogeneous networks that are necessarily dynamic. What's more, most social networks and communities tend to engage in positive reinforcement, not debate, so the groups encourage groupthink. No one in the group wants to confront others and if they do they are often ostracized from the group. Social media platforms offer the promise of innovation, but can become highly scaled cliques of very similar people with very similar ideas and experiences. A closed network of people with similar values and experiences eventually becomes stagnant. Only when new people are injected into that network, people who have different experiences and perspectives, and those folks are willing to express their ideas, will the network create new ideas.
It's not just networks, or the number of interactions that matter. If that were the case, IBM or General Motors would be highly innovative. In a social network, innovation is influenced by the range of experience of the nodes, how dynamic the entire network is, and how willing the network is to experience new ideas and different perspectives.