Network Laws

Last week I spoke at Dr. Natalie’s social business class at UCLA and one of the presenters who was on before me commented on the idea that people have a finite number of connections they can maintain, if I recall correctly he said 123 connections. What he is referring to is something called Dunbar’s Number, which asserts that the number of relationships a person can maintain is limited by the human brains cognitive abilities to between 100 and 230, with 150 being the commonly quoted number.

I have no reason to dispute this and would defer to Dunbar’s research in this area however it is vitally important to recognize a couple of facts about the human condition, which is that we are, as a species, amazingly adaptable and complex in our interactions with other people. This is where Dunbar’s Number falls short for me, which is that we do not have the same intensity of relationship with each person we have a relationship with.

Dunbar’s Number is unique among the various network laws which are often quoted, unique because it doesn’t deal with the economic utility of a network but rather our ability to scale a social graph. The other 3 laws which come up in these discussions build on prior work and take into account technological advances.

Sarnoff’s Law: This is named after television executive David Sarnoff who observed that broadcast networks have economic potential that is proportional to the number of participants. Simply put a broadcast network that can reach 100 people is 10x more valuable than one with 10 people.

Metcalfe’s Law: Along with Moore’s Law this is the most cited law in computer science and very clearly builds on Sarnoff’s Law. Where Sarnoff’s Law is proportional, Metcalfe’s is exponential. The utility of a network is equivalent to the square of the number of participants. Metcalfe’s Law is well covered so I’ll leave it at that.

Reed’s Law: Of all the network laws this one is the most interesting to me and it goes directly to the idea that Dunbar’s Number understates the capacity of people to maintain very large social graphs. What Reed’s Law stipulates is that the value of the network is increases exponentially, in proportion to 2n, rather than n2 as Metcalfe states.

Beckstrom’s Law: This one is interesting because of the specific measure that Beckstrom has developed, which is that the value of a network is the net value added for each transaction multiplied by all the members of that network. Where it gets interesting is on two dimensions, the first being that the net value added is combinatorial, as in all the participants in a transaction derive value from the transaction, and that the network itself has a virtuous cycle in that the more participants it has the more value it has which then becomes an attractor for more people to join (think Facebook here).

What I find appealing about Reed’s Law is that it recognizes that people belong to multiple network groups and have a wide range of weak and strong connections online. Dunbar’s Number makes an implicit assumption that we have a finite number of maintainable connections and each connection requires an equal investment for maintenance, or that we have a finite amount of cognitive ability and each connection chips away at that total. Reed’s Law circumvents this by recognizing that we get value from the group as well as the individual connections contained within…. so in short I find that it is possible to maintain far more than 150 network connections.