scholarly journals General connectivity distribution functions for growing networks with preferential attachment of fractional power

2007 ◽  
Vol 48 (11) ◽  
pp. 113303
Author(s):  
Kazumoto Iguchi ◽  
Hiroaki S. Yamada
Keyword(s):  
Preferential Attachment ◽  
Fractional Power ◽  
Distribution Functions ◽  
Growing Networks ◽  
Connectivity Distribution

scholarly journals TRANSPORT EQUATIONS FROM LIOUVILLE EQUATIONS FOR FRACTIONAL SYSTEMS

2006 ◽  
Vol 20 (03) ◽  
pp. 341-353 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Transport Equation ◽  
Fractional Power ◽  
Distribution Functions ◽  
Fractional Dimension ◽  
Fractional Systems ◽  
Dimension Space ◽  
Bogoliubov Equations ◽  
Reduced Distribution Functions ◽  
Gasdynamic Equations ◽  
Generalized Transport Equation

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Gasdynamic equations for fractional systems are derived from the generalized transport equation.

Scale-free growing networks imply linear preferential attachment

2001 ◽  
Vol 65 (1) ◽  
Author(s):  
Kasper Astrup Eriksen ◽  
Michael Hörnquist
Keyword(s):  
Preferential Attachment ◽  
Scale Free ◽  
Growing Networks

scholarly journals FOKKER–PLANCK EQUATION FOR FRACTIONAL SYSTEMS

2007 ◽  
Vol 21 (06) ◽  
pp. 955-967 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Phase Space ◽  
Power Systems ◽  
Fractional Power ◽  
Planck Equation ◽  
Distribution Functions ◽  
Fractional Integrals ◽  
Fractional Systems ◽  
Fokker Planck Equation ◽  
Bogoliubov Equations ◽  
Fokker Planck

The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usual phase space. The generalizations of the Bogoliubov equations are derived from the Liouville equation for fractional (power) systems. Using these equations, the corresponding Fokker–Planck equation is obtained.

scholarly journals The evolution of network topology by selective removal

2005 ◽  
Vol 2 (5) ◽  
pp. 533-536 ◽  
Author(s):  
Marcel Salathé ◽  
Robert M May ◽  
Sebastian Bonhoeffer
Keyword(s):  
Network Topology ◽  
Biological Networks ◽  
Preferential Attachment ◽  
Protein Interaction Networks ◽  
Interaction Networks ◽  
Network Growth ◽  
Scale Free ◽  
The Past ◽  
The World ◽  
Growing Networks

The topology of large social, technical and biological networks such as the World Wide Web or protein interaction networks has caught considerable attention in the past few years (reviewed in Newman 2003 ), and analysis of the structure of such networks revealed that many of them can be classified as broad-tailed, scale-free-like networks, since their vertex connectivities follow approximately a power-law. Preferential attachment of new vertices to highly connected vertices is commonly seen as the main mechanism that can generate scale-free connectivity in growing networks ( Watts 2004 ). Here, we propose a new model that can generate broad-tailed networks even in the absence of network growth, by not only adding vertices, but also selectively eliminating vertices with a probability that is inversely related to the sum of their first- and second order connectivity.

scholarly journals Coexistence in Preferential Attachment Networks

2016 ◽  
Vol 25 (6) ◽  
pp. 797-822 ◽  
Author(s):  
TONĆI ANTUNOVIĆ ◽  
ELCHANAN MOSSEL ◽  
MIKLÓS Z. RÁCZ
Keyword(s):  
Real World ◽  
Preferential Attachment ◽  
Theoretical Models ◽  
Qualitative Feature ◽  
Large Networks ◽  
New Model ◽  
Growing Networks ◽  
Attachment Model

We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses neighbours by preferential attachment, and selects its type based on the number of initial neighbours of each type. The model is analysed in detail, and in particular, we determine the possible proportions of the various types in the limit of large networks. An important qualitative feature we find is that, in contrast to many current theoretical models, often several competitors will coexist. This matches empirical observations in many real-world networks.

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