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Detectability constraints on meso-scale structure in complex networks.

¹Department of Computer Science, University of Exeter, Exeter, United Kingdom.

|January 22, 2025

Summary

This summary is machine-generated.

The configuration model restricts detecting core-periphery structures in networks. This study derives conditions for detecting such meso-scale structures and links block modularity optimization to stochastic block models.

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Area of Science:

Network Science
Graph Theory
Statistical Physics

Background:

Understanding large network organization relies on node partitions like community, core-periphery, and disassortative structures.
Meso-scale structures provide insights into network function and organization.

Purpose of the Study:

To investigate common meso-scale structures using block modularity.
To analyze the impact of the configuration model on detecting core-periphery and nested structures.
To establish an equivalence between block modularity optimization and degree-corrected Stochastic Block Model parameter estimation.

Main Methods:

Analysis of network structures using block modularity.
Derivation of inequalities to determine detectability of structures under the configuration model.
Establishment of a general equivalence between block modularity optimization and maximum likelihood estimation for the degree-corrected Stochastic Block Model.

Main Results:

The configuration model imposes significant constraints on detecting core-periphery and related structures in both directed and undirected networks.
Derived inequalities indicate that the detectability of these structures is limited and related to the resolution limit.
Nestedness, a structure related to core-periphery, is also found to be detectable only under specific conditions.
A formal equivalence is established between optimizing block modularity and maximum likelihood estimation in the degree-corrected Stochastic Block Model.

Conclusions:

The configuration model presents inherent limitations for identifying core-periphery and nested structures in networks.
The equivalence found provides a framework for contrasting inferential and descriptive approaches to meso-scale structure detection.
This research clarifies the constraints and methodologies for analyzing complex network organization.