Paper Info
Title
Is Preferential Attachment the 2nd Law of Thermodynamics in Disguise?
Abstract
Barabu0027asi-Albertu0027s `Scale Freeu0027 model is the accepted theory of the evolution of real world networks. Careful comparison of the theory with a wide range of real world graphs, however, has identified shortcomings in the predictions of the theory when compared to the data. particular, the exponent $gamma$ of the power law distribution of degree is predicted by the model to be identically 3, whereas the data has values of $gamma$ between 1.2 and 2.9. The degree distribution data also tends to fall off at high degrees, which indicates the existence of maximal node degrees for many networks. In this paper we propose a simple extension to the `Scale Freeu0027 model, which offers far better agreement with the experimental data. This improvement is satisfying, but the model still does not explain why the attachment probabilities should favor high degree nodes, or indeed how constraints arrive in non-physical networks. Using recent advances in the analysis of the entropy of graphs at the node level we propose a first principles derivation for the `Scale Freeu0027 and `constraintsu0027 model from thermodynamic principles, and demonstrate that both preferential attachment and constraints are simply a natural consequence of the 2nd law of thermodynamics.
Year
Venue
Field
2016
arXiv: Physics and Society
Theoretical physics,Second law of thermodynamics,Scale-free network,Mathematics,Preferential attachment
DocType
Volume
Citations 
Journal
abs/1612.03115
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Phil Tee100.68
Ian Wakeman2436129.40
George Parisis312216.44
J. H. P. Dawes4101.95