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  1. Home > Articles & Issues >
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  3. The Degree Distribut ...
Conference paper

The Degree Distribution of Thickened Trees

Michael Drmota (1), Bernhard Gittenberger (1), Alois Panholzer (1)
(1) Institut für Diskrete Mathematik und Geometrie [Wien]
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Imported on
May 10, 2017
Published on
December 31, 2007
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Proceedings
DOI
10.46298/dmtcs.3561
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https://about.hal.science/hal-authorisation-v1
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The Degree Distribution of Thickened Trees

Michael Drmota (1), Bernhard Gittenberger (1), Alois Panholzer (1)
(1) Institut für Diskrete Mathematik und Geometrie [Wien]
Abstract
We develop a combinatorial structure to serve as model of random real world networks. Starting with plane oriented recursive trees we substitute the nodes by more complex graphs. In such a way we obtain graphs having a global tree-like structure while locally looking clustered. This fits with observations obtained from real-world networks. In particular we show that the resulting graphs are scale-free, that is, the degree distribution has an asymptotic power law.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • scale free networks
  • recursive trees
  • generating functions
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