SPATIAL GIBBS RANDOM GRAPHS

• 成果类型: Article
• 署名作者: Mourrat, Jean-Christophe; Valesin, Daniel
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); University of Groningen
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1316
• 发表日期: 2018
• 页码: 751-789
• 关键词: long-range percolation; connectivity; emergence; networks; diameter; neuroanatomy; uniqueness; MODEL

摘要

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with small average graph distance between vertices, but adding an edge comes at a cost measured according to the geometry of the ambient physical space. In most cases, we identify the order of magnitude of the average graph distance as a function of the parameters of the model. As the proofs reveal, hierarchical structures naturally emerge from our simple modeling assumptions. Moreover, a critical regime exhibits an infinite number of discontinuous phase transitions.