My answer to this question is in the context of my "work" network. For this purpose, I use a simple rating system comprised of two components, Relevance and Enthusiasm. 
I rate a Relevant Contact a 1 if they actually have control over assignments or work I might want to do, a 2 if they have a great vantage point and a 3 if they have neither control nor vantage point. Hence, a low score is better in terms of Relevance. 
I rate an Enthusiastic Contact a 1 if they were or are a co-worker, a 2 if they were or are a closely dealt with outsider, a 3 if they are a by reputation only contact or a 4 if they are a non business contact. Again, a low score is better in terms of Enthusiasm.
A contact who scores 2 is one of the most "effective" contacts in my network in terms of being helpful with my obtaining assignments or work I might want to do.
This scoring is not something I necessarily do on an excel spread sheet; it is an exercise I might undertake more casually. Regardless, I know my network includes a significant number of contacts with low scores and I am grateful.
How does your network rate when you look at it from this perspective? Do you use another system to rate you own network of contacts? I would love to "hear" about it.
And I would love to "hear" your thoughts in terms of building a more effective network.