2021/11/25 by Xiongye Xiao, Hanlong Chen, Paul Bogdan · 63 citations
Physics and Astronomy · Economics, Econometrics and Finance · Biochemistry, Genetics and Molecular Biology · Mathematics · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Bioinformatics and Genomic Networks #Computer science #Complex network #Complex system #ENCODE #Multifractal system #Interdependent networks #Theoretical computer science #Topology (electrical circuits) #Network topology #Formalism (music) #Node (physics) #Distributed computing #Construct (python library) #Fractal #Artificial intelligence #Mathematics #Computer network
paper · pdf · doi:10.1038/s41598-021-02203-4
published in Scientific Reports 11(1), 22964 (Nature Portfolio)
openalex publication_date 2021/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Network theory helps us understand, analyze, model, and design various complex systems. Complex networks encode the complex topology and structural interactions of various systems in nature. To mine the multiscale coupling, heterogeneity, and complexity of natural and technological systems, we need expressive and rigorous mathematical tools that can help us understand the growth, topology, dynamics, multiscale structures, and functionalities of complex networks and their interrelationships. Towards this end, we construct the node-based fractal dimension (NFD) and the node-based multifractal analysis (NMFA) framework to reveal the generating rules and quantify the scale-dependent topology and multifractal features of a dynamic complex network. We propose novel indicators for measuring the degree of complexity, heterogeneity, and asymmetry of network structures, as well as the structure distance between networks. This formalism provides new insights on learning the energy and phase transitions in the networked systems and can help us understand the multiple generating mechanisms governing the network evolution.