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Shape Measures of Random Increasing k-trees



Random increasing k-trees represent an interesting and useful class of strongly dependent graphs that have been studied widely, including being used recently as models for complex networks. In this paper we study an informative notion called BFS-profile and derive, by several analytic means, asymptotic estimates for its expected value, together with the limiting distribution in certain cases; some interesting consequences predicting more precisely the shapes of random k-trees are also given. Our methods of proof rely essentially on a bijection between k-trees and ordinary trees, the resolution of linear systems, and a specially framed notion called Flajolet–Odlyzko admissibility.



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A complete version containing an appendix on zero distribution of the indicial polynomial and another on random generation of random k-trees can be found on the second author's webpage. This version will be referred to as DHS throughout this paper.



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Shape Measures of Random Increasing k-trees



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