states that the value of a network is proportional to the square of the number of nodes in that network. This is true of networks where every node is connected to every other node. A more generalized formulation of Metcalf's law would be: the value of a network is equal to the number of connections (also known as edges) in that network. (An even better definition would try to incorporate a measurement of the value of each connection – e.g. two people who communicate a lot probably value that connection more than two people who don't).
It is widely understood that the resilience of chemical molecules or architectural structures is a function of not just their materials but also their structures. The same is true of information networks like social networks, marketplaces, and communication networks. Two networks with the same number of nodes (e.g. users) and same number of edges (e.g. relationships of Friending or Following) might have very different levels of resilience or – as is it's normally called in business contexts – defensibility.
Suppose we define the defensibility of a networked web service as: The minimum number of users a competitor needs to capture in order to capture 80% of the value of the service.
I picked 80% somewhat arbitrarily. To measure defensibility more precisely you'd want to plot the distribution where one axis is number of users and the other axis is the number of edges each user has (I attempt this superficially here
). Also note I am simplifying what Twitter and Facebook have evolved into as services. On Twitter, there are explicit edges (Following) but also lots of "soft edges", e.g. when someone @ replies a user she doesn't follow. Facebook has evolved from being a purely "undirected graph" (Friending) to being a hybrid network with the introduction of Liking and Following.
Networks like Facebook tend to have a low variation in the number of connections (Friends) per user compared to networks like Twitter where some people have many millions of followers but most people have less than 100. Academics would say Twitter is a far more "centralized
" network than Facebook.
In that sense Twitter is far less defensible than Facebook. If a rival can capture, say, ten thousand of the top Twitter users, they might be able to capture 80% of the value that followers of those users get from the service.
Recently someone in charge of Google+ tweeted: "We’re about to pilot a ‘suggested user’-like mechanism on Google+. If you’ve got more than 100k followers on Twitter, DM me – lets talk!". This is a smart strategy that recognizes the primary vulnerability in Twitter's network structure.
Services competing with Facebook are better off trying to exploit clusters (e.g. geographic, demographic, interests) versus going after more "central" (popular) users.
I am far from being an expert on the academic literature on social network analysis but from my research I haven't found anything that looks at the structures of networks from a business point of view. Interesting topics might be: the strength and weakness of various structures, strategies for attacking and defending those structures, historical case studies on how networks grew or decayed, and so on. Perhaps someone can point me to relevant research if it exists.