# Ordered increasing $k$-trees: Introduction and analysis of a preferential attachment network model

Abstract : We introduce a random graph model based on $k$-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of important parameters for the network model such as the degree, the local clustering coefficient and the number of descendants of the nodes and root-to-node distances. We do not only obtain results for random nodes, but in particular we also get a precise description of the behaviour of parameters for the $j$-th inserted node in a random $k$-tree of size $n$, where $j=j(n)$ might grow with $n$. The approach presented is not restricted to this specific $k$-tree model, but can also be applied to other evolving $k$-tree models.
Keywords :
Type de document :
Communication dans un congrès
Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.549-564, 2010, DMTCS Proceedings
Domaine :

Littérature citée [15 références]

https://hal.inria.fr/hal-01185576
Contributeur : Coordination Episciences Iam <>
Soumis le : jeudi 20 août 2015 - 16:32:43
Dernière modification le : mardi 7 mars 2017 - 15:07:55
Document(s) archivé(s) le : mercredi 26 avril 2017 - 10:12:00

### Fichier

dmAM0138.pdf
Fichiers éditeurs autorisés sur une archive ouverte

### Identifiants

• HAL Id : hal-01185576, version 1

### Citation

Alois Panholzer, Georg Seitz. Ordered increasing $k$-trees: Introduction and analysis of a preferential attachment network model. Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.549-564, 2010, DMTCS Proceedings. 〈hal-01185576〉

### Métriques

Consultations de la notice

## 91

Téléchargements de fichiers