Preferential attachment
They are also referred to under the names Yule process, cumulative advantage, the rich get richer, and the Matthew effect.
The principal reason for scientific interest in preferential attachment is that it can, under suitable circumstances, generate power law distributions.
[1] If preferential attachment is non-linear, measured distributions may deviate from a power law.
[2] These mechanisms may generate distributions which are approximately power law over transient periods.
A classic example of a preferential attachment process is the growth in the number of species per genus in some higher taxon of biotic organisms.
This is the primary reason for the historical interest in preferential attachment: the species distribution and many other phenomena are observed empirically to follow power laws and the preferential attachment process is a leading candidate mechanism to explain this behavior.
Preferential attachment is considered a possible candidate for, among other things, the distribution of the sizes of cities,[7] the wealth of extremely wealthy individuals,[7] the number of citations received by learned publications,[8] and the number of links to pages on the World Wide Web.
Qualitatively it is intended to describe not a mechanical multiplicative effect like preferential attachment but a specific human behavior in which people are more likely to give credit to the famous than to the little known.
The classic example of the Matthew effect is a scientific discovery made simultaneously by two different people, one well known and the other little known.
It is claimed that under these circumstances people tend more often to credit the discovery to the well-known scientist.
Thus the real-world phenomenon the Matthew effect is intended to describe is quite distinct from (though certainly related to) preferential attachment.
The first rigorous consideration of preferential attachment seems to be that of Udny Yule in 1925, who used it to explain the power-law distribution of the number of species per genus of flowering plants.
Yule was able to show that the process gave rise to a distribution with a power-law tail, but the details of his proof are, by today's standards, contorted and difficult, since the modern tools of stochastic process theory did not yet exist and he was forced to use more cumbersome methods of proof.
Most modern treatments of preferential attachment make use of the master equation method, whose use in this context was pioneered by Simon in 1955, in work on the distribution of sizes of cities and other phenomena.
The application of preferential attachment to the growth of the World Wide Web was proposed by Barabási and Albert in 1999.
