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)

Stefan Felsner (ed.)

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

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,
, 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.
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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
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