The fittest node: Who will "grab all the links" and "shape the network into a star"?

“The explosive success of “new kid on the block” Google could not be explained by the scale-free model until a measure of a node’s ability to stay in front of the competition produced a “fitness model.” Examining the fitness model data, Ginestra Bianconi was startled to find that the calculations used were very similar to those found in the formation of a Bose-Einstein condensate. The math describing the behavior of “Bose gases” (a unique creature of sub-atomic quantum mechanics) turned out to be identical to those in the network fitness model. This similarity means, according to Barabasi, that in certain circumstances, particularly fit nodes in a network did not merely get richer … the winner could take all.

In an ordinary “fit-get-rich” network, the fittest node gets biggest, but other fit nodes are close behind, so that “the power laws and the fight for links are not antagonistic but can coexist peacefully.” Id. 102. In a “winner-takes-all” system, the fittest node grabs all the links, shaping the network into a “star” or “hub and spoke” topology which is not scale free … there is a single hub and many tiny nodes. These findings have obvious relevancy to those studying antitrust law and policy and the ongoing case of Microsoft.” (Source)