From David P. Reed’s “That Sneaky Exponential – Beyond Metcalfe’s Law to the Power of Community Building“:
Bob Metcalfe, inventor of the Ethernet, is known for pointing out that the total value of a communications network grows with the square of the number of devices or people it connects. This scaling law, along with Moore’s Law, is widely credited as the stimulus that has driven the stunning growth of Internet connectivity. Because Metcalfe’s law implies value grows faster than does the (linear) number of a network’s access points, merely interconnecting two independent networks creates value that substantially exceeds the original value of the unconnected networks. …
But many kinds of value are created within networks. While many kinds of value grow proportionally to network size and some grow proportionally to the square of network size, I’ve discovered that some network structures create total value that can scale even faster than that. Networks that support the construction of communicating groups create value that scales exponentially with network size, i.e. much more rapidly than Metcalfe’s square law. I will call such networks Group-Forming Networks, or GFNs. …
What kind of value are we talking about, when we say the value of a network scales as some function of size? The answer is the value of potential connectivity for transactions. That is, for any particular access point (user), what is the number of different access points (users) that can be connected or reached for a transaction when the need arises. …
The value of potential connectivity is the value of the set of optional transactions that are afforded by the system or network. …
Metcalfe’s law, simply derived, says that if you build a network so that any customer can choose to transact with any other customer, the number of potential connections each of the N customers can make is (N-1), giving a total number of potential connections as N(N-1) or N2-N. Assuming each potential connection is worth as much as any other, the value to each user depends on the total size of the network, and the total value of potential connectivity scales much faster than the size of the network, proportional to N2. …
In networks like the Internet, Group Forming Networks (GFNs) are an important additional kind of network capability. A GFN has functionality that directly enables and supports affiliations (such as interest groups, clubs, meetings, communities) among subsets of its customers. Group tools and technologies (also called community tools) such as user-defined mailing lists, chat rooms, discussion groups, buddy lists, team rooms, trading rooms, user groups, market makers, and auction hosts, all have a common themeâ€â€they allow small or large groups of network users to coalesce and to organize their communications around a common interest, issue, or goal. Sadly, the traditional telephone and broadcast/cable network frameworks provide no support for groups. …
What we see, then, is that there are really at least three categories of value that networks can provide: the linear value of services that are aimed at individual users, the “square” value from facilitating transactions, and exponential value from facilitating group affiliations. What’s important is that the dominant value in a typical network tends to shift from one category to another as the scale of the network increases. Whether the growth is by incremental customer additions, or by transparent interconnection, scale growth tends to support new categories of killer apps, and thus new competitive games. …
What’s important in a network changes as the network scale shifts. In a network dominated by linear connectivity value growth, “content is king.” That is, in such networks, there is a small number of sources (publishers or makers) of content that every user selects from. The sources compete for users based on the value of their content (published stories, published images, standardized consumer goods). Where Metcalfe’s Law dominates, transactions become central. The stuff that is traded in transactions (be it email or voice mail, money, securities, contracted services, or whatnot) are king. And where the GFN law dominates, the central role is filled by jointly constructed value (such as specialized newsgroups, joint responses to RFPs, gossip, etc.). …
I’d like to close with a speculative thought. As Francis Fukuyama argues in his book Trust, there is a strong correlation between the prosperity of national economies and social capital, which he defines culturally as the ease with which people in a particular culture can form new associations. There is a clear synergy between the sociability that Fukuyama discusses and the technology and tools that support GFNs-both are structural supports for association. As the scale of interaction grows more global via the Internet, isn’t it possible that a combination of social capital and GFN capital will drive prosperity to those who recognize the value of network structures that support free and responsible association for common purposes?