Sparse Popularity Adjusted Stochastic Block Model
This work addresses the need for more detailed sparsity patterns in network analysis, which is incremental as it builds on the recently introduced PABM.
The paper tackles the problem of modeling sparse networks with block structures by introducing a model that allows for structural sparsity, where some connection probabilities are zero while others remain above a threshold, providing a more nuanced view compared to existing models like SBM and DCBM.
In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes only the behavior of network as a whole, without distinguishing between the block-dependent sparsity patterns. To the best of our knowledge, the recently introduced Popularity Adjusted Block Model (PABM) is the only block model that allows to introduce a {\it structural sparsity} where some probabilities of connections are identically equal to zero while the rest of them remain above a certain threshold. The latter presents a more nuanced view of the network.