Measure for degree heterogeneity in complex networks and its application to recurrence network analysis
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Summary
This summary is machine-generated.We introduce a new method to measure degree heterogeneity in complex networks using only their degree distribution. This novel measure quantifies network complexity and can be applied to various network types, including chaotic attractors.
Area Of Science
- Network Science
- Complex Systems Analysis
- Graph Theory
Background
- Understanding the structural properties of complex networks is crucial for analyzing their behavior.
- Degree heterogeneity, a measure of degree distribution diversity, is a key network characteristic.
- Existing methods for quantifying degree heterogeneity can be computationally intensive or topology-dependent.
Purpose Of The Study
- To propose a novel, computationally efficient measure for degree heterogeneity in unweighted, undirected complex networks.
- To demonstrate the measure's applicability across diverse network topologies, including synthetic and real-world networks.
- To validate the measure's utility in comparing the structural complexity of recurrence networks derived from chaotic attractors.
Main Methods
- Developed a new measure of degree heterogeneity requiring only the degree distribution.
- Introduced a limiting network for analytical definition and normalization of the measure to the interval [0, 1].
- Applied the measure to synthetic (random, scale-free) and real-world networks, numerically studying variations with network parameters (N, p, γ).
Main Results
- The proposed measure increases with node degree diversity and is applicable to all network topologies.
- Heterogeneity values were computed for synthetic and real-world networks, normalized between 0 and 1.
- Numerical studies confirmed the measure's behavior with varying network parameters (N, p, γ).
Conclusions
- The novel degree heterogeneity measure offers a simple yet powerful tool for network analysis.
- It provides a single index to compare structural complexity, particularly useful for recurrence networks from chaotic attractors.
- This measure enhances the ability to analyze and compare diverse complex systems based on their topological features.