Complex Network Characterization Using Graph Theory and Fractal Geometry: The Case Study of Lung Cancer DNA Sequences

• Published in: Applied sciences Vol. 10; no. 9; p. 3037
• Main Authors: Babic, Matej, Mihelic, Jurij, Cali, Michele
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-05-2020
• Subjects: Angiogenesis; Base sequence; bioengineering; Biology; Case studies; complex networks; Complexity; Deoxyribonucleic acid; DNA; DNA geometry; DNA methylation; Fractal analysis; fractal dimension; Fractal geometry; Fractals; Genes; Genetic aspects; Genetic engineering; Geometry; Graph theory; Hypoxia; Lung cancer; Medical prognosis; Medical research; Nucleotide sequence; Pattern recognition; Theory; topological properties; Topology; Transcription factors; Tumors; Slovenia
• ISSN: 2076-3417; 2076-3417
• DOI: 10.3390/app10093037

This paper discusses an approach developed for exploiting the local elementary movements of evolution to study complex networks in terms of shared common embedding and, consequently, shared fractal properties. This approach can be useful for the analysis of lung cancer DNA sequences and their properties by using the concepts of graph theory and fractal geometry. The proposed method advances a renewed consideration of network complexity both on local and global scales. Several researchers have illustrated the advantages of fractal mathematics, as well as its applicability to lung cancer research. Nevertheless, many researchers and clinicians continue to be unaware of its potential. Therefore, this paper aims to examine the underlying assumptions of fractals and analyze the fractal dimension and related measurements for possible application to complex networks and, especially, to the lung cancer network. The strict relationship between the lung cancer network properties and the fractal dimension is proved. Results show that the fractal dimension decreases in the lung cancer network while the topological properties of the network increase in the lung cancer network. Finally, statistical and topological significance between the complexity of the network and lung cancer network is shown.