Paper Info
Title
Hamiltonian Dynamics of Preferential Attachment.
Abstract
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment (PA), known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton's equations. We derive the explicit form of the Hamiltonian that governs network growth in PA. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales.
Year
DOI
Venue
2015
10.1088/1751-8113/49/10/105001
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Keywords
Field
DocType
complex networks,preferential attachment,Hamiltonian dynamics,exponential random graphs
Network science,Random graph,Network dynamics,Quantum mechanics,Geometric networks,Complex network,Degree distribution,Hamiltonian mechanics,Mathematics,Preferential attachment
Journal
Volume
Issue
ISSN
49
SP10
1751-8113
Citations 
PageRank 
References 
2
0.39
1
Authors
3
Name
Order
Citations
PageRank
Konstantin Zuev1132.09
Fragkiskos Papadopoulos235222.97
Dmitri V. Krioukov3423.91