2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 239244
author:  Zoran Nikoloski , Narsingh Deo and Ludek Kucera 

title:  Degreecorrelation of Scalefree graphs 
keywords:  degreecorrelation, scalefree degree distribution, linearized chord diagrams 
abstract: 
Barabási and Albert [1] suggested modeling
scalefree networks by the following random graph process:
one node is added at a time and is connected to an earlier
node chosen with probability proportional to its degree. A
recent empirical study of Newman [5] demonstrates existence
of degreecorrelation between degrees of adjacent nodes in
realworld networks. Here we define the degree
correlationcorrelation of the degrees in a pair of
adjacent nodesfor a random graph process. We determine
asymptotically the joint probability distribution for
nodedegrees,
d
and
d'
, of adjacent nodes for every
0≤d≤ d'≤n
, and use this result to show that the model of
Barabási and Albert does not generate
degreecorrelation. Our theorem confirms the result in
[KR01], obtained by using the meanfield heuristic
approach.
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reference:  Zoran Nikoloski and Narsingh Deo and Ludek Kucera (2005), Degreecorrelation of Scalefree graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 239244 
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