## 1 Introduction  
Aging can be defined as the time-related deterioration of the physiological functions necessary for survival and fertility [1]. While the specific mechanisms underlying aging are still being studied, it has been shown that mitochondrial DNA (mtDNA) plays a crucial role. In fact, mitochondrial dysfunction, including decreased oxidative capacity and increased oxidative damage, is thought to substantially contribute to biological aging [2, 3]. This is due to the higher rate of genomic variants and less efficient repair machinery compared to nuclear DNA: mtDNA's mutation rate is up to 15 times higher than that of nuclear DNA [4]. For this matter, _Drosophila melanogaster_ has been crucial in advancing our understanding of this physiological process and has become a widely used model organism that hasdistinct advantages in aging research [5]. Commonly known as the fruit fly, it can provide many advantages as a model for research [6] because of the several characteristics that enable it to be widely used in many different applications: low cost of rearing and housing, absence of regulatory oversight for their use in experiments, ease of generating large populations, well-defined dietary requirements, easily quantified reproductive output, distinct tissues that can be dissected and genetically manipulated, and furthermore, some of their tissues are equivalent to many of those found in mammals [6]. It is worth remarking that _Drosophila_ has significantly helped in studying the hallmarks of aging (genomic instability, telomere attrition, epigenetic alterations, loss of proteostasis, deregulated nutrient sensing, mitochondrial dysfunction, cellular senescence, stem cell exhaustion, and altered intercellular communication [7]). Since 1983, in fact, several studies have been conducted on components of the insulin and IGF-1 like signaling (IIS) pathway in order to genetically manipulate the lifespan of worms and flies with some mutations that were found to be effective in extending their lifespan [8; 9]. This eventually led to the identification of polymorphisms in the insulin pathway transcription factor FOXO associated with the length of life in humans [10]. Furthermore, it has been demonstrated that IGF-1 signaling alters mitochondrial function and enhances their fitness. This includes the maintenance of mitochondrial DNA/RNA [11]. In a biological system, molecules and genes cooperate to perform various biological functions. They engage in dynamic interactions, and graphs are a formal representation of this interaction. In mathematics, a graph is a structure made up of a set of _nodes_ or _vertices_ and a set of _edges_ or _arcs_ that show pairwise relationships between the nodes and vertices. The mathematical theory that lies behind graphs has its origins in recreational math problems, but it has now become a significant area of mathematical research with applications in various fields, including computational biology. In computational biology, graph theory is used to represent and analyze complex biological systems such as protein-protein interactions, gene regulatory networks, and metabolic pathways. By representing biological systems as graphs, researchers can use graph algorithms and metrics to study the structural and functional properties of these networks, predict new interactions, and identify key network components that may be targeted for drug development. This discipline has led to many important discoveries, such as the identification of disease-causing genes and the development of new drugs, and has allowed \"network medicine\" to grow and develop. Network medicine is an interdisciplinary field that aims to understand the complexity of biological systems by mapping out the interactions between genes, proteins, and other molecular components. The field uses an integrated, network-based, systems biology-driven approach to define the etiology of complex diseases, reclassify complex diseases, and develop new treatments and preventive strategies [12].