Reed's Law is arguing that the number of cliques I can participate in on a social network is more important than the number of "friends". The number of cliques tends to grow exponentially in the number of users except:
(i) Social networks are extremely sparse.. the most well connected nodes have 5000 out of hundreds of millions of users. This greatly reduces then number of available cliques (although does still leave it exponential).
(ii) Many of the connections are quite weak.. my interest in a random clique of a social graph in which I'm a member is almost always zero.
(iii) Most cliques that provide value can be extended into other cliques by inviting members, so I may only be interested in maximal cliques, a further significant winnowing.
(iv) Cliques aren't even the greatest representation of this because most groups I participate in on a social network don't have all-to-all friending.
On the whole though I expect the effect of disinterest in most cliques, and improving the interested one's to optimality by extension reduces the cliques I'm actually interested to something far slower than exponential.
(i) Social networks are extremely sparse.. the most well connected nodes have 5000 out of hundreds of millions of users. This greatly reduces then number of available cliques (although does still leave it exponential).
(ii) Many of the connections are quite weak.. my interest in a random clique of a social graph in which I'm a member is almost always zero.
(iii) Most cliques that provide value can be extended into other cliques by inviting members, so I may only be interested in maximal cliques, a further significant winnowing.
(iv) Cliques aren't even the greatest representation of this because most groups I participate in on a social network don't have all-to-all friending.
On the whole though I expect the effect of disinterest in most cliques, and improving the interested one's to optimality by extension reduces the cliques I'm actually interested to something far slower than exponential.