Degrees in Preferential Attachment Networks with an Anomaly

2025/05/06 by Qiu Liang, Remco van der Hofstad, Liang, Qiu +3
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2505.03340

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/08/01

Abstract

We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural properties of the network. The anomaly is such that after its arrival it attracts newly added edges with fixed probability. We investigate the growth of degrees in the network, finding that the anomaly's degree increases almost linearly. We also provide a heuristic derivation for the exponent of the limiting degree distributions of ordinary vertices, and study the degree growth of the oldest vertex. We show that when the anomaly enters early, the degree distribution is altered significantly, while a late anomaly has minimal impact. Our analysis provides deeper insights into the evolution of preferential attachment networks with an anomalous vertex.

Citations

• Fluctuation Bounds for Continuous Time Branching Processes and Evolution of Growing Trees With a Change Point
• Semi-Supervised Classification with Graph Convolutional Networks

Cited by

• Likelihood-based anomaly detection in preferential attachment networks

Related

• Random networks with sublinear preferential attachment: Degree evolutions
• Characterizing the head of the degree distributions of growing networks
• Expected degree of finite preferential attachment networks
• Learning growth mechanisms of tail realistic preferential attachment models from network degree distributions
• Structural Properties of the Geometric Preferential Attachment Model