Youngseok Song | Searcharxiv

arXiv2026

nethist: An R package for Nonparametric Graphon Estimation via Network Histograms

Understanding the generative mechanism of real-world networks is crucial for analyzing connection patterns and making inference from network data. Graphons are widely used to model such mechanisms. Network histogram methods are nonparametric approaches based on blockmodel approximations that provide an intuitive view of network connection structures. However, there is a lack of software packages that construct network histograms. We introduce the R package nethist, which implements network histogram-type graphon estimators within a unified interface. This package is applicable to both single-layer and multilayer networks, and includes graphical summaries for examining both local and global network structures. By providing comprehensive network analysis tools, nethist facilitates understanding of complex systems of interrelated vertices.

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arXiv2026

Joint Estimation of Sparse Multilayer Networks via Graph Limits

Network datasets in modern applications often involve multiple types of interactions occurring over a shared set of individuals. Characterizing the generating mechanisms of these interactions can be enhanced by joint modelling, as shared vertices allow layers to help explain the structure of other layers. We model multiplex observations using graph limits, called a scaled set of graphons, and develop a nonparametric joint estimator based on blockmodel approximations, termed the multi-network histogram. This nonparametric framework captures each layer's varying sparsity and connection structure, accounting for heterogeneity via shared latent variables across all layers. We establish the theoretical properties of the multi-network histogram, providing an upper bound for the weighted mean integrated squared error and deriving the optimal bandwidth that minimizes this error. By leveraging information across layers, this joint modelling achieves a reduction in error and a smaller optimal bandwidth, which enables high-resolution estimation even in sparser layers. Its usefulness is demonstrated through simulation studies and an application to socioeconomic networks in an Indian village.

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