Networks form through usage and must be maintained through it
I recently read The network's the thing (via, itself probably via). One of the things this article is about is how for many companies, the network created by your users is the important piece, not the product itself; you can change the product but retain the network and win, despite the yelling of aggravated users. My impression is that this is a popular view of companies, especially companies with social networks.
(Purely social networks are not the only sort of networks there are. Consider Github; part of its value is from the network of associations among users and repositories. This is 'social' in the sense that it involves humans talking to each other, but it is not 'social' in the sense that Twitter, Facebook, and many other places are.)
On the one hand, this "networks matter but products don't" view is basically true. On the other hand, I think that this is a view that misses an important detail. You see, users do not form (social) networks on services out of the goodness of their hearts. Instead, those social networks form and remain because they are useful to people. More than that, they don't form in isolation; instead they're created as a side effect of the usefulness of the service itself to people, and this usefulness depends on how the service works (and on how people use it). People create the network by using the product, and the network forms only to the extent and in the manner that the product is useful to them.
As a corollary, if the product changes enough, the network by itself will not necessarily keep people present. What actually matters to people is not the network as an abstract thing, it's the use they get out of the network. If that use dries up because the product is no longer useful to them, well, there you go. For example, if people are drawn to Twitter to have conversations and someday Twitter breaks that by changing how tweets are displayed and threaded together so that you stop being able to see and get into conversations, people will drift away. Twitter's deep social network remains in theory, but it is not useful to you any more so it might as well not exist in practice.
In this sense, your network is not and cannot be separated from your core product (or products). It exists only because people use those products and they do that (in general) because the products help them or meet some need they feel. If people stop finding your product useful, the network will wither. If different people find your product useful in different ways, the shape of your (active) network will shift.
(For example, Twitter's network graph will probably look quite different if it becomes a place where most people passively follow a small number of 'star' accounts and never interact with most other people on Twitter.)
At the same time, changes in the product don't necessarily really change the network because they don't necessarily drastically change the use people get out of the service. To pick on Twitter again, the length of tweets or whether or not their length counts people mentioned in them are not crucial to the use most people get out of Twitter, for all that I know I heard yelling about both.