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2019

Agglomeration in a preferential attachment random graph with edge-steps

Alves, Caio, Ribeiro, Rodrigo, Sanchis, Remy

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In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps.

More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a vertex-step occurs) or with probability $1-p$ an edge connecting two existent vertices is added (an edge-step occurs).
We prove that the global clustering coefficient decays as $t^{-\gamma(p)}$ for a positive function $\gamma$ of $p$.
We also prove that the clique number of these graphs is, up to sub-polynomially small factors, of order~$t^{(1-p)/(2-p)}$.

Agglomeration in a preferential attachment random graph with edge-steps · Around

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A-L. Barabási and R. Albert · 1999
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Growing scale-free networks with tunable clustering
B. Kim and P. Holme · 2002
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Mathematical results on scale-free random graphs. in handbook of graphs and networks: From the genome to the internet
B. Bollobás and O. Riordan · 2003
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