Time-varying network models
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.
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