We are all busy people so each of us needs to make the best use of our time. The same is true about building business relationships. Focus your efforts on building relationships that matter most.
Be strategic about who you meet and / or build a relationship with so you can be efficient and effective. It is too easy to get in relationships with lots of people. We meet new people every day at events, the office, from referrals, online, etc.
You should pick and choose who you interact wtih. While it important to have a big and diverse network, make sure to have the right people who are complementary and ones who you can help and vice versa.
Spend time figuring out who you want to meet and then find out how to get in front of these people. LinkedIn is a great tool for finding out someone's business background. Find a way to get an introduction from one of your LinkedIn contacts.
Also, figure out which associatiations, charities, or events that someone is involved in so you can meet in person. Make it a point to introduce yourself at a gathering.
The more strategic you focus your relationship building efforts the more you will build a good quality network. Build the relationships that matter most.