Thank you all. Yes, I have just felt relationship is the same with Guanxi, although in marketing literatrues, scholars still try to distinguish the two terms
Unlike in job market, which needs your professor to make a call, in the application the connections are usually embedded in your recommendation letters or the previously constructed relationships. So the letters are very important.
Like it or not, relationship is an inevitable part of lives. The difference may be how well-regulated and upon what is it built. It can be built on relative simple relationship in some countries, whereas it can also built on exchange of economical or other kind of interests. It benefits if it is used in the right way.
Networking is only part of your application pacakage. If you have it, that is good, and it may help you get the offer. If you don't, it is still OK. You have enough chance to convince the professors that you are a good PhD candidate.