Consider your existing professional network and its breadth. Now, consider how many of these individuals are experienced, highly competent and accomplished persons. Next, consider how many of these persons would take your call and thoughtfully respond to it simply on the basis of the mutual respect you have for each other. If this list doesn't contain many names, I'm guessing that your professional networks is much broader than it is deep.
How does one deepen their professional network? It can take considerable time and numerous interactions for connections to decide if they trust, respect or even like each other. Beyond simply mixing it up, is the value that the parties create for each other over time.
A friend and colleague of mine John Ruhlin (http://www.ruhlingroup.com) recently recommended that I read Derek Coburn's terrific book, "Networking is Not Working". The book discusses the author's core premise that traditional networking efforts are generally not especially productive uses of time. Instead, he argues that one should work in a deliberate fashion to create value for their existing network. This can take the form of recommending new clients to your current clients. It can also involve identifying resources to address your clients' and network partners' varied needs. In other words, we should each work to create sustained and tangible value for our network and our clients to make it extremely difficult for competitors to displace us.
We may currently do some of these things on an intuitive level. Coburn's book encourages us to be much more deliberate about the practice.