Constraints and entropy in a model of network evolution

Tee, Philip, Wakeman, Ian, Parisis, George, Dawes, Jonathan and Kiss, István Z (2017) Constraints and entropy in a model of network evolution. European Physical Journal B: Condensed Matter and Complex Systems. ISSN 1434-6028 (Accepted)

[img] PDF - Accepted Version
Restricted to SRO admin only

Download (878kB)

Abstract

Barab´asi-Albert’s ‘Scale Free’ model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however, indicates that the model is in some cases, only a rough approximation to the dynamical evolution of real networks. In particular, the exponent γ of the power law distribution of degree is predicted by the model to be exactly 3, whereas in a number of real world networks it has values between 1.2 and 2.9. In addition, the degree distributions of real networks exhibit cut offs at high node degree, which indicates the existence of maximal node degrees for these networks. In this paper we propose a simple extension to the ‘Scale Free’ model, which offers 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 Free’ and ‘constraints’ model from thermodynamic principles, and demonstrate that both preferential attachment and constraints could arise as a natural consequence of the second law of thermodynamics.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
School of Mathematical and Physical Sciences > Mathematics
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering > TK5101 Telecommunication Including telegraphy, telephone, radio, radar, television > TK5105.5 Computer networks. General works
Depositing User: Georgios Angelos Parisis
Date Deposited: 31 Aug 2017 14:12
Last Modified: 13 Sep 2017 13:53
URI: http://sro.sussex.ac.uk/id/eprint/69952

View download statistics for this item

📧 Request an update