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Topological energy of networks
1School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China and Collaborative Innovation Center of Statistical Data Engineering, Technology & Application, Zhejiang Gongshang University, Hangzhou 310018, China.
Chaos (Woodbury, N.Y.)
|April 25, 2023
Summary
This study introduces topological energy (TE), a new network indicator that uses higher-order node information. TE effectively distinguishes network structures and is robust to minor changes, showing potential for real-world applications.
Area of Science:
- Network Science
- Graph Theory
- Data Analysis
Background:
- Network energy, derived from adjacency matrix eigenvalues, is a key network indicator.
- Existing methods primarily consider immediate neighbor information.
Purpose of the Study:
- To expand the definition of network energy to incorporate higher-order network information.
- To introduce Topological Energy (TE) as a novel network indicator.
Main Methods:
- Utilizing resistance distances to quantify node-to-node distances.
- Employing order complexes to extract higher-order structural information.
- Defining Topological Energy (TE) based on resistance distances and order complexes.
Main Results:
- Topological Energy (TE) effectively distinguishes between graphs with identical spectra.
- TE demonstrates robustness against small, random perturbations in network edges.
- Real-world network energy curves significantly differ from random graph curves, validating TE's discriminative power.
Conclusions:
- Topological Energy (TE) serves as a robust indicator for differentiating network structures across multiple scales.
- TE offers potential applications in analyzing and distinguishing complex real-world networks.
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