2: INCREASING RETURNS
A network's tendency to explode in value mathematically
was first noticed by Bob Metcalfe, the inventor of a localized networking technology called Ethernet. During the late 1970s Metcalfe was selling a combination of Ethernet, Unix, and TCP/IP (the internet protocol), as a way to make large networks out of many small ones. Metcalfe says, "The idea that the value of a network equals n squared came to me after I failed to get networks to work on a small scale, despite many repeated experiments." He noticed that networks needed to achieve critical mass to make them worthwhile. But he also noticed that as he linked together small local networks here and there, the value of the combined large network would multiply abruptly. In 1980 he began formulating his law: value = n x n.
In fact, n2 underestimates the total value of network growth. As economic journalist John Browning notes, the power of a network multiplies even faster than this. Metcalfe's observation was based on the idea of a phone network. Each telephone call had one person at each end; therefore the total number of potential calls was the grand sum of all possible pairings of people with phones. But online networks, like personal networks in real life, provide opportunities for complicated three-way, four-way, or many-way connections. You can not only interact with your friend Charlie, but with Alice and Bob and Charlie at the same time. The experience of communicating simultaneously with Charlie's group in an online world is a distinct experience, separate in its essential qualities, from communicating with Charlie alone. Therefore, when we tally up the number of possible connections in a network we have to add up not only all the combinations in which members can be paired, but also all the possible groups as well. These additional combos send the total value of the network skyrocketing. The precise arithmetic is not important. It is enough to know that the worth of a network races ahead of its input.
This tendency of networks to drastically amplify small inputs leads to the second key axiom of network logic: the law of increasing returns. In one way or another this law undergirds much of the strange behavior in the network economy. The simplest version goes like this: The value of a network explodes as its membership increases, and then the value explosion sucks in yet more members, compounding the result.
Okay, I freely admit that math is not my forte. But what's the difference between:
value = n squared
and
value = n x n
My understanding was that n squared = n x n. Yes?
Or is the bottom line really: "The precise arithmetic is not important."
Hi Kate,
This law says for every new member your network grows quadratically,
Have a look at below link, this paper explains network theory in greater detail.
http://www.spectrum.ieee.org/print/4109
It argues how much more valuable a network becomes as it grows.
Worth mentioning the type of network you are valuing but it uses a model that is a slower (more accurate) rate than Metcalfe, Maths is n log(n)
N
When I first discovered the internet in 1989, I could communicate with people in different countries more efficiently than with people I knew. No one I knew was interested in this medium of communication. They were buying fax machines.
A more recent example of this trend is the growth of Facebook. When I first joined, it was to communicate with my children and the mature adults were not part of the community.
Now we are all on Facebook, and I enjoy the updates from my friends. As each network grows it becomes more interesting and offers more variety.
Now I wonder what is next. . .
Disclaimer: Read only if you really want to think about the math behind this:
I would bet that the correct equation is NOT a quadratic one at all, but an exponential one, modified for the limited amount of time and attention we each really have. If you have two people in your network, the number of relationships available is 1x2 which is two.That is to say, that each individual can have a relationship with each OTHER individual. If you have three, the number is 1x2x3, which is six, not nine, as would be the case in nxn. However..... If four people are in your network, the number of relationships that are part of that network are 1x2x3x4 if you have five, the number of relationships is 1x2x3x4x5 So far, we are at 120, NOT 25, which would be the result of nxn. The trick is that eventually, you get to a point where the individual's capacity for relating is exceeded. My fiance has 20,000 myspace "friends" and does NOT have relationships with them all. They are advertising prospects, not relationships, and their value is lesser than the ones with whom he has actual relationships. On facebook I have just over 600 friends, ALL of whom I have some sort of real life connection to, though some are more real, or more active, than others. If each of these 600 people ALSO had relationships with each other, that would be 1.2655723162254307425418678245151e+1408 possible relationships. Assuming that they don't, but that they have relationships with a similar number of real humans, the numbers are similar, even though the total number of people in the network is much larger. Hence the appearance of the nxn phenomenon.