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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Completeness of Community Structure in Networks.

Jia-Rong Xie¹, Pan Zhang², Hai-Feng Zhang³

¹Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China.

Scientific Reports

|July 15, 2017

Summary

We introduce exclusive modularity, a new metric for network community structure completeness. Expert-defined communities can be surprisingly incomplete, highlighting the need to re-evaluate metadata

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Area of Science:

Network Science
Statistical Physics
Data Analysis

Background:

Community structure is fundamental to understanding complex networks.
Existing methods for evaluating community structure completeness have limitations.
The relationship between network metadata and its inherent community structure requires deeper investigation.

Purpose of the Study:

To develop a mathematically principled method for assessing the completeness of community structure in networks.
To introduce a novel metric, exclusive modularity, for quantifying community structure completeness.
To evaluate the completeness of expert-defined and algorithm-generated network partitions.

Main Methods:

Definition of exclusive modularity, a new measure for community structure.
Application of the cavity method from statistical physics.
Utilizing a null model based on the degree-corrected stochastic block model.

Main Results:

Demonstrated that expert-defined partitions can be surprisingly incomplete in real-world networks, such as the political blogs network.
Indicated a need to re-examine the relationship between metadata and community structure in networks.
Exclusive modularity shows independent interest as a novel metric.

Conclusions:

The developed method provides a principled way to determine the completeness of network community structure.
Expert annotations do not always fully capture the underlying community structure.
Exclusive modularity has potential applications in detecting hidden and hierarchical structures and network embedding.