Reed's law

Reed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network . Reed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network . The reason for this is that the number of possible sub-groups of network participants is 2N − N − 1, where N is the number of participants. This grows much more rapidly than either so that even if the utility of groups available to be joined is very small on a per-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system. Given a set A of N people, it has 2N possible subsets. This is not difficult to see, since we can form each possible subset by simply choosing for each element of A one of two possibilities: whether to include that element, or not. However, this includes the (one) empty set, and N singletons, which are not properly subgroups. So 2N − N − 1 subsets remain, which is exponential, like 2N.