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

Matej Babič,Michele Calì,Jurij Mihelič

doi:10.3390/app10093037

Abstract

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.

Highlights

Theoretical models on complex networks have assumed a key role in numerous disciplines, ranging from computer science, physics, sociology, engineering, and medicine, to molecular, population biology, and deoxyribonucleic acid (DNA) sequences analysis [1,2]
This paper introduces an initial presentation of the concepts of graph theory, fractals, and pattern recognition for their possible use in the calculation of statistical and topological properties of the DNA network and the characterization of DNA sequences in lung cancer
This study investigated the functional role of HIF1A between exons and introns and the connection between these polymorphisms and lung cancer risk by using fractal geometry and graph theory

Summary

Introduction

Theoretical models on complex networks have assumed a key role in numerous disciplines, ranging from computer science, physics, sociology, engineering, and medicine, to molecular, population biology, and deoxyribonucleic acid (DNA) sequences analysis [1,2]. In the classical conception of DNA geometry, the double helix represents a ribbon constructed from smooth curves describing an idealized structure. How to read and recognize the primary structure of a DNA sequence seems to be a fundamental problem. DNA sequencing and fragment assembly have received a much more specific attention for improving the reconstruction of full strands of DNA focused on the pieces of data to record. The concept of graph theory and fractal geometry are proposed a particular way of analyzing DNA sequences and their properties. Many scientific papers [3] dealing with DNA sequences analysis [4] have been published. The main aim of the work is to outline the advantage of applying graph theory and fractals in the study of lung cancer DNA sequences

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Conclusion