## Why Pseudo Friends Decrease Social Network Values

Path: mv.asterisco.pt!mvalente
From: mvale…@ruido-visual.pt (Mario Valente)
Newsgroups: mv
Subject: Why Pseudo Friends Decrease Social Network Values
Date: Wed, 11 Mar 08 23:30:21 GMT

Everyone must agree that social networks provide enormous
value to its participants. And its pretty clear that the value
of a social network will be larger depending on the number of
participants: the more people there are in a network, the more
value it can provide.

But does the value of a social network derive simply from
the number of participants? Or shouldnt we consider that some
value is aditionally derived from the number of connections

For each of the two referred ways of measuring network
value, we have previous proposals: Metcalfe’s law and Reed’s
law.

Metcalfe’s law proposes that the value of a (social) network
is proportional to the square of the number of users (N), that
is to say V=N^2. A network with 2 users is valued 4, one with
5 users 25, one with 10 is worth 100.
A similar law states that the value of a network is rather
dependent on the number of unique connections, that is to say
V=N(N-1)/2, but this is asymptotically equivalent to V=N^2.

Another proposal, Reed’s law, states that the value of a
network is much larger that the two previous formulas and
predictions. Reed’s law states the value of a network is really
dependent on the number of possible subgroups of network
participants (users). Mathematically this is expressed as
V=2^N-N-1, which grows much faster than Metcalfe’s law and its
derivation.

Can we thus assume that the value of a social network grows
infinitely? That there’s no upper boundary? That on a network
where everyone is connected to everyone else the value is
astronomical? Wouldnt that mean that instead of waiting for
users to connect to each other, social networking sites should
just go ahead and connect everyone to everybody else?

This obviously goes against common sense. What then is
the value of a social network?

I propose that the value of a network, as per Reed’s law,
is dependent not on the number of possible subgroups but on
the number of *existing* subgroups. This, of course, is a
number between 1 (the whole network is a group) and 2^N-N-1.

This *actual* number of subgroups should then be used as
the number of participants in a meta-network (a network of
groups), with its valued derived from Metcalfe’s law (ie.
V=N^2 or V=N(N-1)/2.

It can thus be shown that people who add friends or
followers (or any other type of connection) without any
type of discrimination are actually decreasing the value of
the network (by decreasing the number of existing subgroups).
Equivalently, social networks who allow for indiscriminate
connections or dont put up any barriers to connectiviy, will
eventually see their value dwindle.

At the limit, where everyone is connected to everyone
else, the value of the network, using the original Metcalfe’s
law is 1 (V=1^2=1). This is certainly kinder than the the
value derived from its equivalent V=N(N-1)/2.

In a social network where everyone is connected to
everyone else, the value of the network is 0.

The people collecting virtual pseudo friends are actually
transforming social networks like Twitter into a tragedy
of the commons.

— MV