Link persistence and conditional distances in multiplex networks.

Area of Science:

• Network science
• Complex systems
• Data analysis

Background:

• Recent studies explored geometric organization in multiplex networks, revealing hyperbolic node coordinate correlations.
• These correlations aided applications like translayer link prediction and mutual navigation.

Purpose of the Study:

• To investigate if geometric correlations are sufficient to explain topological relationships between multiplex network layers.
• To determine the role of link persistence in multiplex network topology.

Main Methods:

• Analysis of real-world multiplex systems to assess correlations between hyperbolic node coordinates and link persistence across layers.
• Modification of a geometric multiplex model to incorporate link persistence.

Main Results:

• Geometric correlations alone are insufficient to explain topological relations between network layers.
• Link persistence across layers is significant in real systems, irrespective of hyperbolic distances.
• The modified model incorporating link persistence accurately reproduces observed behaviors in real multiplexes.
• Link persistence explains high edge overlap between layers, a phenomenon not explained by coordinate correlations alone.

Conclusions:

• Link persistence is a key factor in multiplex network topology, alongside geometric correlations.
• Multiplex embedding methods should consider both coordinate correlations and link persistence for improved performance.
• Understanding link persistence enhances translayer link prediction accuracy.