Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communities

Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testing

“…Unlike the framework of [12,13,17], these two alternative notions of sparsity allow well-defined sparse network models on the entire population, which implies a valid out-of-sample inference. However, rigorous and optimal statistical estimation and inference under these two frameworks are not well developed, except for only a few recent efforts [95,58]. It is natural to ask whether the current state-of-the-art techniques of network analysis discussed in this paper can be modified or generalized to analyze sparse networks in these two alternative exchangeability frameworks.…”

Random clique covers for graphs with local density and global sparsity

“…Under certain choices of W (including those corresponding to the original Caron and Fox [2017] paper), the resulting graphs are sparse and exhibit power law degree distribution. This framework has been extended to incorporate clustering structure [Herlau et al, 2016, Todeschini et al, 2016.…”

“…This type of behavior is a key component of "small world" graphs [Watts and Strogatz, 1998]. While extensions to the sparse exchangeable graphs [Herlau et al, 2016, Todeschini et al, 2016 and the edge-exchangeable graphs [Williamson, 2016] incorporate community-type structure, they do not yield this form of transitivity.…”

Sparse Networks with Core-Periphery Structure

“…Firstly, we provide a precise definition of what it means for a graph to have a core-periphery structure, based on the sparsity properties of the subgraphs of core and periphery nodes. Secondly, building on earlier work from [37], we present a class of sparse network models with such properties, and provide methods to simulate from this class, and to perform posterior inference. Finally, we demonstrate that our approach can detect meaningful core-periphery structure in two real-world airport and trade networks, while providing a good fit to global structural properties of the networks.…”

“…Sparse graph models with (overlapping) block structure have already been proposed within the framework of [6] - [18,37]. However, these models cannot be applied directly to model networks with a core-periphery structure, as they make the assumption that a single parameter tunes the overall sparsity properties of the graph, with the same structural sparsity properties across different blocks.…”