Structural Properties of the Geometric Preferential Attachment Model

2025/11/22 by Feng, Chenxu, Li, Yifan
Computer Science · Mathematics · Physics and Astronomy · #05C82 #60D05 #Complex Network Analysis Techniques #FOS: Mathematics #Opportunistic and Delay-Tolerant Networks #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2511.18052

openalex publication_date 2025/11/22 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality constant equal to the ratio of the number of triangles between a random geometric graph and an Erdős-Rényi graph. Furthermore, we prove that the maximum degree grows polynomially with the network size, sharing the same exponent as the standard model; however, the spatial constraint induces a slower growth rate in the network's early evolution. Finally, we extend prior results on connectivity and diameter to the case of networks with finite out-degrees.

Citations

• Geometric preferential attachment in non-uniform metric spaces
• The Clustering Coefficient of a Scale-Free Random Graph

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