https://hal.inria.fr/hal-01185576Panholzer, AloisAloisPanholzerInstitut für Diskrete Mathematik und Geometrie [Wien] - TU Wien - Vienna University of TechnologySeitz, GeorgGeorgSeitzInstitut für Diskrete Mathematik und Geometrie [Wien] - TU Wien - Vienna University of TechnologyOrdered increasing $k$-trees: Introduction and analysis of a preferential attachment network modelHAL CCSD2010network modelincreasing $k$-treesdegree distributionlocal clustering coefficientroot-to-node distanceslimiting distributions[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]Episciences Iam, CoordinationDrmota, Michael and Gittenberger, Bernhard2015-08-20 16:32:432021-10-13 19:58:042015-08-24 10:03:58enConference papershttps://hal.inria.fr/hal-01185576/document10.46298/dmtcs.2778application/pdf1We 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.