Closed network is an alternative to an open network. An individual who has a closed network is someone whose contacts all know each other. Most of us tend to exist in closed networks, as it is simpler to maintain them. Why? Because we tend to hang around with people who know each other and if some of our friends don't know each other it is easier for us to let them meet one another, than to keep them separated. Put simply, it is far easier to organize one big party and invite all friends there (so that they get to know each other), than to organize multiple small parties where we invite groups of people who don't know each other.
If all of your friends (or acquaintances) in an organization know each other, then you are likely to be in a closed network and you are unlikely to be able to generate many innovative ideas. However, closed networks are better at providing emotional support and enforce the norms of collaboration. That is, if your friends know each other, it is more difficult for one of them to cheat on the others and not to provide you with help when you request it.
Open and closed networks are useful for different things. Open networks provide access to new information while closed networks provide you with emotional support and help. Ideally, one's network should combine the elements of open and closed networks. You should build the networks such that some of your friends know each other, while the others don't. You get help and support from the part of your network that contains the contacts who know each other, while you get innovative ideas from the people who don't know each other.
In other words, you need to be strategic in how you build your personal networks within your firm and only then you can derive your own personal competitive advantage from them.