Zoran Nikoloski ; Narsingh Deo ; Ludek Kucera

Degreecorrelation of Scalefree graphs
dmtcs:3406 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

https://doi.org/10.46298/dmtcs.3406
Degreecorrelation of Scalefree graphs
Authors: Zoran Nikoloski ^{1}; Narsingh Deo ^{1}; Ludek Kucera ^{2}
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Zoran Nikoloski;Narsingh Deo;Ludek Kucera
1 School of Electrical Engineering and Computer Science [Orlando]
2 Department of Applied Mathematics (KAM)
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 \textitdegree correlation―correlation of the degrees in a pair of adjacent nodes―for a random graph process. We determine asymptotically the joint probability distribution for nodedegrees, $d$ and $d'$, of adjacent nodes for every $0≤d≤ d'≤n^1 / 5$, 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.
Akama, Hiroyuki, 000000031777497; Miyake, Maki; Jung, Jaeyoung; Murphy, Brian, 2015, Using Graph Components Derived From An Associative Concept Dictionary To Predict fMRI Neural Activation Patterns That Represent The Meaning Of Nouns, Plos One, 10, 4, pp. e0125725, 10.1371/journal.pone.0125725.
Gustedt, Jens, 2009, Generalized Attachment Models For The Genesis Of Graphs With High Clustering Coefficient, Complex Networks, pp. 99113, 10.1007/9783642012068_9.
Lee, DuanShin; Chang, ChengShang; Zhu, Miao; Li, HungChih, 2019, A Generalized Configuration Model With Degree Correlations And Its Percolation Analysis, Applied Network Science, 4, 1, 10.1007/s4110901902402.
Lee, DuanShin; Chang, ChengShang; Li, HungChih, 2019, A Generalized Configuration Model With Degree Correlations, Complex Networks X, pp. 4961, 10.1007/9783030144593_4.