jcoombes / barabasi_albert Goto Github PK

In this project you will study a standard model for a growing network. A simple version ofthis model was described by Barab ́asi and Albert (1999) [1] but it is identical to the citationnetwork model of Price (1965) [2]. In terms of the degree distribution, these models arein turn completely equivalent to the models of Yule (1925) [3] and Simon (1955) [4]. The central idea is that the fat tails seen in many areas could be explained in terms of a “richget richer” principle. This concept goes back to the 19th Century (at least) when Paretonoted that 80% of the land in Italy was owned by just 20% of the population. The idea isso universal that it occurs in many different guises — the “Pareto principle”, the “80-20rule” or even then Matthew effect (Matthew’s gospel “For everyone who has will be givenmore”). For simplicity we will use the terminology of Barab ́asi and Albert [1] who talkaboutpreferential attachmentand we will refer to this model as theBA model.This is so our language matches that of most recent network literature though it fails to acknowledge previous contributions sufficiently [1] A.-L. Barab ́asi and R. Albert,Emergence of scaling in random networks Science,286173 (1999).[2] D. J. de S. Price,The scientific foundations of science policy, Nature,206233–238(1965).[3] G. U. Yule,A mathematical theory of evolution based on the conclusions of Dr.J.C. Willis, F.R.S. Phil. Trans. B,21-8721–87 (1925).[4] H.A. Simon,On a class of skew distribution functions, Biometrica,42425 (1955).

License: MIT License