Beyond being a connector (as Malcolm Gladwell mentioned in his book "Tipping Point"), how do you become a next level networker? Having more contacts? Strengthening your network?
The answer is: forming triads. What is a triad? A triad (explained in "Tribal Leadership") is when you introduce two people to each other. There may be no direct benefit for you, but the idea is to create a bond between two people you know so they might form a connection. The indirect benefit of this is you being the source of the connection. If networking is truly about giving, not receiving, than a triad is one of the purest forms of connecting out there.
The downside is your ego. Use the example of leadership. Most people desire to be labeled as a leader. Yet, the most effective leaders don't talk about themselves as leaders, but are more concerned about developing those around them. The "followers" of the leader determine how effective the leader is. The hard part is true leadership is more about succession than success.
You can apply the same principle to networking. You and I would rather connect for personal benefit, not to help others and get potentially nothing back in return. The challenge is to take your ego out of the situation and be focused on helping others succeed. Lately, I've experienced triads myself. It's fun to connect two people who can mutually benefit from each other. Consider the larger your network, the more opportunities you can form triads. It doesn't mean you have to physically introduce the two people in person (although it is the most powerful way). You can also do it via email or social media.
Remember, think of networking as a lifestyle, not a task. If it's a task, you'll do it with an end in mind. Instead, why wouldn't you want to connect with more people for the rest of your life? The next level networker isn't concerned with getting the credit. Be genuine. What matters is the heart. What two connections can you introduce today?