Log24

“Perhaps people will revert to private social networks–ones they manage locally….

Perhaps the law of networks–the strength of a tie degrades by the square of the number of links–would become more apparent, and perhaps that would be a good thing.

I’m not sure how good that is as a business model, but it works as a social model.”

The beautiful, brilliant, and charming Esther Dyson seems to have suffered a temporary lapse in brilliance with the above remark on the strength of ties in social networks….

“the law of networks–the strength of a tie degrades by the square of the number of links….”

Here are some useful references encountered while fact-checking Ms. Dyson’s assertion about the “law of networks” —

Links on Graph Theory and Network Analysis

The Navigability of Strong Ties:
Small Worlds, Tie Strength and Network Topology (pdf)

Modeling Coleman’s Friendly Association Networks (pdf)

The Strength of Weak Ties:
A Network Theory Revisited (pdf)

Scientific Collaboration Networks, II (pdf)
(Deals specifically with tie-strength computation.) 

Dynamic Visualization of Social Networks

and, finally, a diagram of social networks in Shakespeare that conclusively demonstrates that there is no simple relationship between strength of ties and number of ties:

Cleopatra’s Social Ties (png)

Perhaps what Ms. Dyson had in mind was the following (courtesy of The Motley Fool):

“Metcalfe’s Law of Networks states that the value of a network grows by the square of the size of the network. Translated, this means that a network that is twice as large as another network will actually be at least four times as valuable. Why? Because four times as many interconnections are possible between participants in the larger network.

When you add a fourth person to a group of three, you don’t add just one more networked relationship. You add several. The new individual can network with all three of the existing persons, and vice versa. The Internet is no different. It became more and more valuable as the numbers of computers using it grew.”

For another perspective on this alleged law, from science fiction author Orson Scott Card, see The Group, a Log24 entry of Sept. 24, 2002.

Elsewhere, in a discussion of social-networking software:

“Esther Dyson starts with a request that people turn to their left and ask the person next to them, ‘Will you be my friend?’ The room erupts in chatter, but, of course, the problem is we don’t have enough information about one another to make a snap decision about that question.”

Obviously, ties resulting from such a request will be weak, rather than strong.  However, as study of the above network-theory links will reveal, weak ties can sometimes be more useful than strong ties.  An example:

Passing the Peace at Mass.

Compare and contrast with
Ms. Dyson’s request to turn and
ask the Mr. Rogers question,
“Will you be my friend?”

The best response to this question
that I know of was contained in
a good-bye letter from a girl named
Lucero in Cuernavaca
in the early 1960’s:

“Si me deveras quieres,
deja me en paz.”

(See Shining Forth.)