Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

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.