| author: | Zoran Nikoloski , Narsingh Deo and Ludek Kucera |
|---|---|
| title: | Degree-correlation of Scale-free graphs |
| keywords: | degree-correlation, scale-free degree distribution, linearized chord diagrams |
| abstract: |
Barabási and Albert [1] suggested modeling
scale-free 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 degree-correlation between degrees of adjacent nodes in
real-world networks. Here we define the degree
correlation---correlation of the degrees in a pair of
adjacent nodes---for a random graph process. We determine
asymptotically the joint probability distribution for
node-degrees,
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
degree-correlation. Our theorem confirms the result in
[KR01], obtained by using the mean-field heuristic
approach.
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| reference: | Zoran Nikoloski and Narsingh Deo and Ludek Kucera (2005), Degree-correlation of Scale-free 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. 239-244 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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