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Consistency of community structure in complex networks.

Maria A Riolo^1,2, M E J Newman^1,2,3

¹Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.

Physical Review. E

|June 25, 2020

Summary

Community detection methods can appear unreliable due to varying results. However, these network structures are consistent, built from invariant "building blocks" that offer significant insight into network organization.

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Area of Science:

Network Science
Data Mining
Computational Social Science

Background:

Traditional community detection methods optimize objective functions to find network partitions.
Focusing solely on the single optimal community structure may overlook valuable information.
Varying results from these methods can be misinterpreted as unreliability.

Purpose of the Study:

To investigate the consistency of community structures derived from optimizing objective functions.
To propose a method for identifying underlying, invariant components within network communities.
To demonstrate that diverse community structures can be consistently explained by common 'building blocks'.

Main Methods:

Analysis of multiple high-scoring community structures, not just the single optimum.
Development of an information theoretic approach to identify community 'building blocks'.
Application and demonstration of the proposed method on various network examples.

Main Results:

Identified that different community structures are assembled from a set of largely invariant 'building blocks'.
Demonstrated that these 'building blocks' represent groups of nodes consistently found together.
Showcased the utility of the information theoretic method in discovering these blocks across networks.

Conclusions:

Community detection methods, despite yielding varied structures, provide consistent insights into network organization.
The concept of invariant 'building blocks' reconciles the apparent inconsistency in community detection results.
The proposed method offers a robust way to understand the fundamental components of network communities.