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

TL;DR

This paper introduces and analyzes a probabilistic k-tree network model with preferential attachment, providing detailed distributional insights into key network parameters and demonstrating applicability to other evolving k-tree models.

Contribution

It presents a new random graph model based on k-trees with a simple combinatorial structure and offers a detailed distributional analysis of network parameters.

Findings

Precise degree distribution analysis

Distribution of local clustering coefficients

Behavior of parameters for the j-th inserted node

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.