Small-world networks: links with long-tailed distributions

Area of Science:

• Complex networks
• Statistical physics
• Network science

Background:

• Small-world networks (SWN) are crucial for modeling complex systems.
• Existing SWN models often use uniform random link additions.
• Understanding network dynamics requires exploring novel network structures.

Purpose of the Study:

• To introduce and analyze a new variant of small-world networks.
• To investigate the impact of chemically dependent link probabilities on network properties.
• To study the behavior of random walkers on these modified networks.

Main Methods:

• Development of a physical model for small-world networks with distance-dependent link probability.
• Assumption of a power-law probability distribution for additional links (AL).
• Analysis of random walker behavior, specifically the probability of return to the origin.

Main Results:

• The probability of random walkers returning to the origin is analyzed.
• A connection is established between the model's outcomes and Levy flights.
• The study highlights how chemical distance influences network topology and dynamics.

Conclusions:

• The proposed SWN variant offers a new perspective on network construction.
• Random walker behavior is significantly affected by chemically dependent link probabilities.
• The findings provide insights into phenomena related to Levy flights in complex systems.