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Updated: Jun 3, 2026
06:56
Generating a Fractal Microstructure of Laminin-111 to Signal to Cells
Published on: September 28, 2020
Spanning trees in a fractal scale-free lattice
Zhongzhi Zhang1, Hongxiao Liu, Bin Wu
1School of Computer Science, Fudan University, Shanghai 200433, China. zhangzz@fudan.edu.cn
Summary
This study reveals the number of spanning trees in a novel fractal scale-free network. Our findings offer insights into the structural properties and dynamics of complex networks with fractality.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Fractal scale-free networks are crucial for understanding complex systems.
- Spanning trees offer insights into network origins and properties.
Purpose of the Study:
- To analytically derive the number of spanning trees in a novel fractal scale-free lattice.
- To investigate the topological characteristics of this unique network model.
- To determine the entropy of spanning trees for this network.
Main Methods:
- Analytical study of topological characteristics.
- Renormalization group technique for enumerating spanning trees.
- Decimation technique for generalization.
Main Results:
- The studied lattice exhibits scale-free, highly clustered, large-world, fractal, and disassortative properties simultaneously.
- Analytical derivation of the number of spanning trees.
- Determination of spanning tree entropy.
Conclusions:
- The findings enhance understanding of structural characteristics and dynamical processes on fractal scale-free networks.
- The employed methods are generalizable to other self-similar deterministic media.
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