Geodesic
Ordered increasing $k$-trees: Introduction and analysis of a preferential attachment network model
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010).

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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. 
@article{DMTCS_2010_special_258_a14,
     author = {Panholzer, Alois and Seitz, Georg},
     title = {Ordered increasing $k$-trees: {Introduction} and analysis of a preferential attachment network model},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
     year = {2010},
     doi = {10.46298/dmtcs.2778},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2778/}
}
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%D 2010
%V DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)
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Panholzer, Alois; Seitz, Georg. Ordered increasing $k$-trees: Introduction and analysis of a preferential attachment network model. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010). doi : 10.46298/dmtcs.2778. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2778/

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