Latent Poisson models for networks with heterogeneous density
This work addresses network analysis challenges for researchers dealing with sparse but locally dense empirical networks, offering incremental improvements in modeling and community detection.
The paper tackled the problem of heterogeneous density in empirical networks, which are globally sparse but locally dense, by introducing latent Poisson models that generate hidden multigraphs to capture this heterogeneity. The result showed that these models are more mathematically tractable than alternatives, enabling disentangling of disassortative degree-degree correlations and improved community structure identification in empirical scenarios.
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense, for example with a few nodes connecting to a large fraction of the rest of the network, or with small groups of nodes with a large probability of connections between them. Here we show how latent Poisson models which generate hidden multigraphs can be effective at capturing this density heterogeneity, while being more tractable mathematically than some of the alternatives that model simple graphs directly. We show how these latent multigraphs can be reconstructed from data on simple graphs, and how this allows us to disentangle disassortative degree-degree correlations from the constraints of imposed degree sequences, and to improve the identification of community structure in empirically relevant scenarios.