Self-organized topology of recurrence-based complex networks

Area of Science:

• Complex Systems Analysis
• Network Theory
• Dynamical Systems

Background:

• Network theory offers novel insights into complex system dynamics.
• Existing methods for network construction from time series primarily focus on adjacency matrices.
• Network geometry derived from adjacency matrices can be variable and lacks inherent structure.

Purpose of the Study:

• To develop a self-organizing approach for deriving steady geometric structures from network adjacency matrices.
• To investigate the factors influencing the self-organization process in recurrence networks.
• To explore the spatial geometry of recurrence networks and its relation to dynamical systems.

Main Methods:

• Simulating recurrence networks as physical systems with edges as springs and nodes as charged particles.
• Employing force-directed algorithms to organize network geometry by minimizing system energy.
• Conducting experiments to analyze the impact of dynamical systems, network construction methods, force-model parameters, and non-homogeneous distributions.

Main Results:

• The self-organized network geometry effectively recovers the attractor of the generating dynamical system.
• The approach provides a novel method for reproducing attractors or time series from recurrence plots.
• New network-theoretic measures, such as average path length and proximity ratio, can be derived from the actual node-to-node distances in the organized topology.

Conclusions:

• Physical models and force-directed algorithms can disclose the inherent spatial geometry of recurrence networks.
• This method bridges network theory and dynamical systems analysis by revealing geometric properties.
• The study provides a new framework for analyzing complex systems and extracting meaningful network-theoretic measures.