Log-periodic oscillations due to discrete effects in complex networks

Area of Science:

• Network Science
• Complex Systems Analysis
• Computational Mathematics

Background:

• Complex networks are ubiquitous in nature and society.
• Understanding network topology and dynamics is crucial.
• Discretization is a common simplification in network modeling.

Purpose of the Study:

• To investigate the impact of discretization on network characteristics.
• To identify and analyze log-periodic oscillations in network metrics.
• To explore the implications of these effects on network optimization.

Main Methods:

• Analysis of internode distances and average path length in discrete network models.
• Comparison with real-world network data (coauthorship, language, food, transport).
• Development of an analytical model to describe observed oscillations.

Main Results:

• Discretization induces log-periodic oscillations in internode distances and average path length.
• These oscillations are consistent across various numerical and real-world networks.
• The analytical description accurately predicts simulation results.

Conclusions:

• Discretization introduces significant, predictable oscillatory behavior in complex networks.
• These discrete effects can lead to non-trivial solutions in network optimization problems.
• The findings offer new insights into network structure and function.