Latent geometry and dynamics of proximity networks
Fragkiskos Papadopoulos1, Marco Antonio Rodríguez Flores1
1Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 3036 Limassol, Cyprus.
Physical Review. E
|December 25, 2019
Summary
A new dynamic-S¹ model reveals that proximity network properties emerge from a latent space, not direct mobility. This model explains power-law distributions and network dynamics, aiding analysis of spreading phenomena.
Area of Science:
- Complex Networks
- Network Science
- Statistical Physics
Background:
- Proximity networks, representing human closeness in physical space, are time-varying graphs crucial for understanding spreading phenomena and routing.
- Despite extensive study, the underlying mechanisms generating observed proximity network characteristics remain unclear.
Purpose of the Study:
- To introduce a novel latent space network model, dynamic-S¹, that explains emergent properties of proximity networks.
- To analytically derive key network distributions and understand the role of network temperature in dynamics.
Main Methods:
- Developed the dynamic-S¹ model, a latent space network model capturing connectivity through hyperbolic geometry, omitting direct node mobility.
- Utilized the model to mathematically prove contact, intercontact, and weight distributions, showing they follow power laws.
- Analyzed the influence of network temperature on distribution exponents and network component formation.
Main Results:
- The dynamic-S¹ model successfully reproduces emergent properties of real-world proximity networks.
- Contact, intercontact, and weight distributions were proven to be power laws in the thermodynamic limit, with exponents matching empirical observations.
- Network temperature was identified as a critical factor influencing network dynamics, degree distributions, and component formation.
Conclusions:
- The dynamic-S¹ model provides a parsimonious explanation for complex proximity network characteristics, driven by latent space geometry rather than explicit mobility.
- The model's analytical tractability facilitates understanding of network dynamics and spreading processes.
- This framework offers potential for developing advanced inference methods for real-world dynamic networks.
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