Maybe it's different in the independent contracting world, but I've found my "network" only semi-helpful in gaining employment. They can give good ideas about companies to try, they can help you refine your resume, and do interview coaching, and if you're lucky they work at the same company you want to apply for so can submit your resume with the "recommend" box ticked, but that's all they seem to be able to do. I've never once had someone in my network who had his hands directly on the "hire this man!" lever at the company.