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Power law of path multiplicity in complex networks
1Department of Systems Science, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China.
PNAS Nexus
|June 19, 2024
Summary
This study introduces path multiplicity, the number of shortest paths, revealing a "hesitant-world" in complex networks. This new metric, following a power-law, offers novel insights beyond traditional network analysis.
Area of Science:
- Network Science
- Graph Theory
- Complex Systems Analysis
Background:
- Complex networks are ubiquitous in nature and society.
- Path properties like length and centrality are well-studied.
- Routing choice diversity in networks remains underexplored.
Purpose of the Study:
- Introduce path multiplicity as a novel network metric.
- Investigate the "hesitant-world" phenomenon in complex networks.
- Characterize the distribution and properties of path multiplicity.
Main Methods:
- Defined path multiplicity as the count of shortest paths between node pairs.
- Conducted extensive empirical investigations on complex networks.
- Analyzed the relationship between path multiplicity and other network metrics.
Main Results:
- Observed a universal power-law distribution for path multiplicity.
- Discovered a "hesitant-world" feature alongside the "small-world" phenomenon.
- Demonstrated that path multiplicity power-law is stronger than node degree power-law.
- Showed existing network models fail to capture these phenomena.
Conclusions:
- Path multiplicity is a distinctive and crucial network metric.
- This metric offers a novel perspective for network design and optimization.
- Findings have potential applications across biological, social, and man-made networks.
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