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Topological measure locating the effective crossover between segregation and integration in a modular network
A Adjari Rad1, I Sendiña-Nadal, D Papo
1École Polytechnique Fédéral de Lausanne, Laboratory of Nonlinear Systems, School of Computer and Communication Science, 1015 Lausanne, Switzerland.
Physical Review Letters
|September 26, 2012
Summary
We developed a new topological measure to detect network segregation and integration crossovers. This measure aligns with dynamical synchronization changes in coupled oscillators, offering a simpler complexity indicator.
Area of Science:
- Network Science
- Complex Systems
- Dynamical Systems
Background:
- Modular networks exhibit both segregation and integration.
- Understanding the crossover between these states is crucial for network dynamics.
- Existing measures of complexity can be computationally intensive.
Purpose of the Study:
- Introduce a computable topological measure for network segregation-integration crossover.
- Correlate this topological measure with dynamical synchronization in coupled oscillators.
- Propose a novel, computationally efficient dynamical measure of complexity.
Main Methods:
- Defined segregation by network modularity and integration by hypergraph algebraic connectivity.
- Analyzed rewiring of equal-sized cliques to observe merging.
- Studied coupled phase oscillators to identify synchronization crossovers.
- Proposed a complexity measure based on intracluster and global synchronization.
Main Results:
- The topological measure effectively locates the segregation-integration crossover.
- This topological crossover coincides with a dynamical crossover in oscillator synchronization.
- The proposed dynamical measure of complexity mimics entropy-based measures but is simpler to compute.
- The measure provides insights into modularity, integration, and network task performance.
Conclusions:
- The proposed topological measure offers a unified approach to understanding network structure and dynamics.
- This measure simplifies complexity assessment in complex systems.
- The findings highlight the interplay between network topology and emergent dynamical behaviors.
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