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Exchangeable random measures for sparse and modular graphs with overlapping communities

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  • Adrien Todeschini
  • Xenia Miscouridou
  • François Caron

Abstract

We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process and naturally generalizes existing probabilistic models with overlapping block structure to the sparse regime. Our construction builds on vectors of completely random measures and has interpretable parameters, each node being assigned a vector representing its levels of affiliation to some latent communities. We develop methods for efficient simulation of this class of random graphs and for scalable posterior inference. We show that the approach proposed can recover interpretable structure of real world networks and can handle graphs with thousands of nodes and tens of thousands of edges.

Suggested Citation

  • Adrien Todeschini & Xenia Miscouridou & François Caron, 2020. "Exchangeable random measures for sparse and modular graphs with overlapping communities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(2), pages 487-520, April.
    • Handle: RePEc:bla:jorssb:v:82:y:2020:i:2:p:487-520
    DOI: 10.1111/rssb.12363
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    Cited by:

    1. Bikramjit Das & Tiandong Wang & Gengling Dai, 2022. "Asymptotic Behavior of Common Connections in Sparse Random Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2071-2092, September.
    2. Caron, François & Panero, Francesca & Rousseau, Judith, 2023. "On sparsity, power-law, and clustering properties of graphex processes," LSE Research Online Documents on Economics 119794, London School of Economics and Political Science, LSE Library.
    3. Liu, Yirui & Qiao, Xinghao & Wang, Liying & Lam, Jessica, 2023. "EEGNN: edge enhanced graph neural network with a Bayesian nonparametric graph model," LSE Research Online Documents on Economics 119918, London School of Economics and Political Science, LSE Library.

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