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We introduce a random graph model based on k-trees, which can be generated byapplying a probabilistic preferential attachment rule, but which also has asimple combinatorial description. We carry out a precise distributionalanalysis of important parameters for the network model such as the degree, thelocal clustering coefficient and the number of descendants of the nodes androot-to-node distances. We do not only obtain results for random nodes, but inparticular we also get a precise description of the behaviour of parameters forthe j-th inserted node in a random k-tree of size n, where j = j(n) might growwith n. The approach presented is not restricted to this specific k-tree model,but can also be applied to other evolving k-tree models.

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