SPATIAL PREFERENTIAL ATTACHMENT NETWORKS: POWER LAWS AND CLUSTERING COEFFICIENTS

• 成果类型: Article
• 署名作者: Jacob, Emmanuel; Moerters, Peter
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); University of Bath
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1006
• 发表日期: 2015
• 页码: 632-662
• 关键词: model

摘要

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent tau > 2. The average clustering coefficient of the networks converges to a positive limit. Finally, a phase transition occurs in the global clustering coefficients and empirical distribution of edge lengths when the power-law exponent crosses the critical value tau = 3. Our main tool in the proof of these results is a general weak law of large numbers in the spirit of Penrose and Yukich.