Personally I would much rather have 1 person that I have fostered a very strong relationship then 10 people who I have weak connections with. I think that quality out beats quantity just about every time.
Some interesting links. There definitely is a point to a lot of weak ties, and I'm sure it works really well for some people. However I do tend to opt more towards a smaller close knit network, probably just my personality but I find that works a lot better for me.