Metcalfe’s Law states that the power of a network increases exponentially as the number of members grows larger. This law is derived from the mathematical graph theory. A graph consists of a collection of vertices (nodes) and edges (that connect pairs of vertices) – what we would call a network. You can calculate with graphs. The so-called "complete graph" is an interesting one, where every node is connected with every other one.
If I have a network of 10 vertices, or contacts, then according the formula, there is a possibility of 10 • (10-1) : 2 = 45 edges between the contacts. A network of 100 contacts can hold a maximum of 4,950 interpersonal relations. How can we use this knowledge? There is an enormous difference between having individual relationships with ten contacts on one hand, and knowing that those ten contacts are mutually connected as well on the other! One does not need much imagination to recognize that the communication force is much stronger in the second case than in the first case. In the second case, my contacts can talk about me among themselves, and, together, they form an opinion about me. This scenario is a lot stronger than a system of individual “lines” (something managers with about ten reporting staff members can think about…).
It is important to realize, with regard to efficiency of networking, that a message (a Tweet for example) sent to ten followers will not always be read by all of them. Too many messages are sent for all of them to be read. I would maintain a “star network” with those ten people, and leave it at that. But because they are connected to each other as well – and you need to encourage your contacts to do that (divide and rule is certainly not the adage here) – my message can still be picked up through another channel. In other words, the denser my network is (or the more complete the graph is), the greater the effectiveness of my communication is in that network.
I have over 9,000 followers on Twitter. According to Metcalfe, I could have 40,495,500 connections among these followers. This means that there is a big chance that a message I send will actually reach as many of those 9,000 followers as possible. But if you realize that those 9,000 followers have followers who do not follow me (are you still following this?), then every retweet is sent to people who do not follow me. Only one of them has to have a couple of thousand followers like me… does that make sense?
In short, make sure that you not only have enough contacts, but encourage them to connect to each other as well. Be a connector! Managers should take note of this as well: do not build a wall around your own employees with the idea that that is the best way for you to manage them. Instead, ensure that the staff of your team or department connect to employees of other teams or departments.
In 1967, the American academic John Milgram published his Six Degrees of Separation theory. According to this notion, someone can be connected to anyone in the world in an average of six steps, from your own friend, through his friend, etc. It is also called the Small World Theory. After a while, it became evident that Milgram’s theory did not work right away, and that certain preconditions were necessary, but the essence of the theory still stands: we are closer to the people we value than we realize. In virtual social networks, we can often approach people we do not know swiftly and directly, without having to be introduced by a mutual friend. Sometimes the social introduction is a retweet or a forward. It is no coincidence that our virtual social networks are called small world networks.
“The significance of weak ties is that they are far more likely to be bridges than are strong ties. It should follow, then, that the occupational groups making the greatest use of weak ties are those whose weak ties do connect to social circles different from one’s own.”
– Sociologist Mark Granovetter in his paper, “The Strength of the Weak Ties: a Network Theory Revised“
According to Granovetter, I do not actually need to maintain a serious social relationship with all my contacts all the time. If my reputation (my personal brand) is sound, people from my network will be inclined to help me if I ask for it, even if I do not know them personally. Such a request for information or help will spontaneously activate a temporary little network out of the larger network – a provisional network. Granovetter writes, “I activate my weak links. The people in question react because they are interested in the subject themselves and want to share their knowledge with me; I have labeled this a resonance network.” With these networks, you can mobilize a kind of collective intelligence. Such resonance networks behave like a neutral network. There are people who process information in networks and subsequently pass it on, and a (subconscious) learning element arises.