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Scale-free growing networks imply linear preferential attachment.
Kasper Astrup Eriksen1, Michael Hörnquist
1NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark. kasper@nordita.dk
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
Summary
Networks with linear preferential attachment exhibit scale-free connectivity. This study proves linearity is essential for this distribution, and preferential linking can apply to node groups, not just individuals.
Area of Science:
- Network science
- Statistical physics
Background:
- Networks grown with linear preferential attachment exhibit scale-free connectivity distributions.
- Understanding the fundamental mechanisms driving scale-free network properties is crucial.
Purpose of the Study:
- To analytically prove the necessity of linearity in preferential attachment for scale-free network distributions.
- To explore variations in preferential linking mechanisms beyond single nodes.
Main Methods:
- Analytical arguments
- Mathematical modeling of network growth
Main Results:
- Linearity in preferential attachment is a necessary condition for scale-free connectivity distributions.
- Preferential linking can be applied to groups of nodes with similar connectivity.
- Time-varying mean connectivity introduces an asymptotically logarithmic deviation from linear linking rates.
Conclusions:
- Confirms the critical role of linear preferential attachment in generating scale-free networks.
- Expands the understanding of preferential attachment to include group-based linking.
- Identifies deviations from linearity in dynamic network environments.