## DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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DMTCS Conference vol AE (2005), pp. 239-244

## 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

### DMTCS Conference Volume AE (2005), pp. 239-244

author: Zoran Nikoloski , Narsingh Deo and Ludek Kucera Degree-correlation of Scale-free graphs degree-correlation, scale-free degree distribution, linearized chord diagrams 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 1 / 5 , 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. If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. 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 For a corresponding BibTeX entry, please consider our BibTeX-file. dmAE0148.ps.gz (69 K) dmAE0148.ps (165 K) dmAE0148.pdf (151 K)