Asymptotic critical transmission radii in random geometry graphs over three-dimensional regions

2025/11/21 by Jie Ding, Ding, Jie, Shuai Ma +7
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Networking and Internet Architecture (cs.NI) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2511.17046

openalex publication_date 2025/11/21 · openalex created_date 2025/11/25 · openalex updated_date 2026/07/28

Abstract

This article presents the precise asymptotical distribution of two types of critical transmission radii, defined in terms of k-connectivity and the minimum vertex degree, for random geometry graphs distributed over three-dimensional regions.

Citations

• Asymptotic Critical Radii in Random Geometric Graphs over Higher-dimensional Regions
• Asymptotic Critical Transmission Radii in Wireless Networks over a Convex Region
• Structural Complexity of One-Dimensional Random Geometric Graphs

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• Asymptotic Critical Radii in Random Geometric Graphs over Higher-dimensional Regions
• Asymptotic Critical Radii in Random Geometric Graphs over 3-Dimensional Convex regions
• Detection of L_∞ Geometry in Random Geometric Graphs: Suboptimality of Triangles and Cluster Expansion
• Scaling of Components in Critical Geometric Random Graphs on 2-dim Torus
• Vertex Degree of Random Geometric Graph on Exponentially Distributed Points