Navigability of temporal networks in hyperbolic space

Area of Science:

• Complex networks analysis
• Network science
• Information theory

Background:

• Information routing is crucial for complex networks.
• Hyperbolic space embeddings aid network navigation.
• Dynamic network structures and their impact on routing are under-explored.

Purpose of the Study:

• To analyze the navigability of real networks with dynamic structures using hyperbolic embeddings.
• To investigate the effect of stochastic node activation-inactivation dynamics on routing efficiency.
• To identify optimal conditions for enhanced navigability in time-varying networks.

Main Methods:

• Employing greedy routing algorithms in hyperbolic space.
• Modeling node behavior with stochastic activation-inactivation dynamics.
• Analyzing navigability metrics such as successful path count and path length.

Main Results:

• Dynamic network structures significantly enhance navigability compared to static ones.
• An optimal intermediate activation probability exists, balancing path success and length.
• Enhanced navigability persists even with high inactivation probability for central nodes.
• Some real networks exhibit 'ultranavigability', maintaining high navigability under extreme unsteadiness.

Conclusions:

• Stochastic dynamics in complex networks can improve information routing efficiency.
• Hyperbolic routing strategies are robust to temporal network variations.
• Findings inform the design of adaptive routing protocols for real-world dynamic networks.