A Generative Model for Extremely Sparse Edge-Exchangeable Networks

Abstract

We propose a graph generative model for sequences of extremely sparse, edge-exchangeable networks. Models for sparse graphs often face a trade-off between desirable properties like exchangeability and the ability to capture the sparsity observed in real-world networks. While models based on vertex or edge exchangeability have successfully generated sparse graphs, achieving the "extremely sparse" regime, where the number of edges scales near-linearly with the number of nodes, has remained a challenge. Recently, a novel Completely Random Measure (CRM) was introduced, demonstrating that this rate could be achieved within the vertex-exchangeable framework of Caron and Fox. This paper extends this work by demonstrating that this new CRM can be integrated into the alternative edge-exchangeable framework to achieve extreme sparsity.