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Simple models of small-world networks with directed links
1Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran. ramzanpour@mehr.sharif.ac.ir
Summary
Directed connections in small-world networks significantly impact information spread. Unfavorable bonds hinder spread, while shortcuts can enhance it, affecting the network's overall accessibility.
Area of Science:
- Network Science
- Complex Systems
- Information Theory
Background:
- Small-world networks exhibit unique topological properties.
- Understanding information propagation is crucial in networked systems.
Purpose of the Study:
- To analyze the impact of directed short- and long-range connections on network spreading processes.
- To quantify the effects of "shortcuts" and "unfavorable bonds" on network accessibility.
Main Methods:
- Development of a simple analytical model for small-world networks.
- Exact calculation of network quantities, including V(T) (sites affected by time T).
- Definition and calculation of the average size of the accessible world.
Main Results:
- Unfavorable bonds negatively impact the spread of information, potentially limiting network-wide propagation.
- Shortcuts have a contrasting, potentially positive effect on spread.
- The interplay between shortcuts and unfavorable bonds determines overall small-world properties.
Conclusions:
- Network structure, specifically directed connections, critically influences spreading dynamics.
- Analytical models provide precise insights into complex network behaviors.
- The balance of connection types dictates the network's capacity to transmit information effectively.