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The Degree Distribution of Thickened Trees

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.
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https://hal.inria.fr/hal-01194676
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Michael Drmota, Bernhard Gittenberger, Alois Panholzer. The Degree Distribution of Thickened Trees. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. pp.149-162. ⟨hal-01194676⟩

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