Time-varying network models
type: Item
instance of: scholarly article
title: Time-varying network models
zbMATH Open document ID: 1323.05115
DOI: 10.3150/14-BEJ617
author: Harry Crane
published in: Bernoulli
publication date: 2015-08-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1507.07664
full work available at URL: https://projecteuclid.org/euclid.bj/1432732033
review text: To model time-varying networks, the author construct exchangeable and consistent Markov processes using a rewiring measure. This exchangeable rewiring process fulfills statistical properties can be constructed as follows. Let \(\mathcal{G}_n\) be the set of graphs (without self-loops) on \(n\) vertices. \(w=((w_{ij}^0,w_{ij}^1))_{1\leq i,j\leq n}\) is an \(n\times n\) symmetric matrix with entries in \(\{0,1\}\times\{0,1\}\) and all diagonal entries \((0,0)\). Its equivalent mapping representation \(w:\mathcal{G}_n\rightarrow\mathcal{G}_n\) is defined as \(w(G)=(w_{ij}^{G_{ij}})_{1\leq i,j\leq n}\), where \(G=(G_{ij})_{1\leq i,j\leq n}\) is the adjacency matrix. Related properties including consistency under sub-sampling, exchangeability, graph limit representation, and the Feller property have been studied.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 05C82
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 6470453
zbMATH Keywords: Aldous-Hoover theorem
zbMATH Keywords: consistency under subsampling
zbMATH Keywords: Erdős-Rényi random graph
zbMATH Keywords: exchangeable random graph
zbMATH Keywords: graph limit
zbMATH Keywords: partially exchangeable array
MaRDI profile type: Publication
arXiv ID: 1507.07664
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OpenAlex ID: W3104236025
description: scientific article