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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Three structural properties reflecting the synchronizability of complex networks.

Kezan Li¹, Michael Small, Kaihua Wang

¹Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 8, 2009

Summary

Network synchronizability in Barabási-Albert (BA) and Watts-Strogatz (WS) networks can be quantified by structural properties. Eccentricity and clustering coefficients positively correlate with synchronizability, while degree distribution variance negatively correlates.

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Area of Science:

Network Science
Complex Systems
Statistical Physics

Background:

Understanding network synchronizability is crucial for analyzing complex systems.
Classical network models like Barabási-Albert (BA) and Watts-Strogatz (WS) exhibit distinct structural properties.

Purpose of the Study:

To statistically quantify the synchronizability of BA and WS networks using structural network properties.
To investigate how adding links affects network synchronizability.
To guide the design of strategies for manipulating network synchronizability.

Main Methods:

Statistical analysis of network synchronizability.
Correlation analysis between structural quantities (eccentricity, degree distribution variance, clustering coefficients) and synchronizability.
Evaluation of link-adding strategies.

Main Results:

Synchronizability of BA and WS networks is statistically quantifiable by eccentricity, variance of degree distribution, and clustering coefficients.
Eccentricity and clustering coefficients show a positive linear correlation with synchronizability.
Variance of the degree distribution shows a negative linear correlation with synchronizability.

Conclusions:

Network structure significantly influences synchronizability.
Specific structural properties can be used to predict and control network synchronizability.
Link-adding strategies can be optimized to achieve desired synchronizability levels.