## 3 Results and Discussion
### Network Analysis  
In order to understand the role of mitochondrial genes in aging, we focused on a cluster that showed a high correlation for any specific life stage and had a higher concentration of mitochondrial genes. As shown in Figure 4, the \"lightsalmon\" cluster (Supplementary Materials Figure S2), despite being a small cluster, contains a high number of mitochondrial genes and shows a positive correlation in the adult male (0.29, \(p\)-value \(<\) 0.05), while a negative one in the embryonic phase (\(-\)0.28, \(p\)-value \(<\) 0.05). The cluster contains 286 genes, and 43 of them are mitochondrial. We studied its topological organization using Syntacle. Several local topological metrics (i.e., degree, betweenness, closeness, and clustering coefficient) were calculated starting from the adjacency matrix generated by WGCNA that was cleaned from values belonging to the lowest ninetieth percentile. This filtering step was adopted to minimize noise and density in the resulting network; the 286 nodes of the network were then wired with 3947 edges, which then represented only strong correlations between genes. This network was made up of 28 components. Figure 3: Relationships between consensus modules and life stages. Each column corresponds to a cluster, and each row to a life stage. The numbers in the table report Pearson correlations and \(p\)-values in parentheses (meant as the probabilities that one would have found the current results if the correlation coefficients were in fact zero, i.e., null hypothesis), where shades of red show a positive correlation and blue shades a negative correlation. First, we assessed the connectivity of each node in the cluster: the mean connectivity of the whole network (2.98) was smaller than the average among all the mitochondrial genes, which is 4.46 (Figure 5). This means that mitochondrial genes tend to be more connected to other nodes in the network: among the top 50 genes, 14 of them were mitochondrial genes, and in the top 10, the mitochondrial ones were 4. The two most connected genes are both mitochondria, i.e., CG7430 (13.58) and UCCR-C1 (ubiquinol-cytochrome c reductase core protein 1) (12.76). Other relevant genes are mAcon1 (5 th) and Pdhb (pyruvate dehydrogenase E1 beta subunit) (8 th). Then, we evaluated the local centrality measures of genes. As for degree centrality, the top 50 genes exhibited an average degree of 67.24, which is higher than the average degree of the whole network (27.60); interestingly, 10 of them were mitochondrial genes. UCCR-C1 was the top mitochondrial gene. Figure 4: Barplot showing the number of nuclear (blue) and mitochondrial (red) genes for each cluster. The lightsalmon cluster has the highest ratio of mitochondrial genes. For what concerns the betweenness centrality, only five mitochondrial genes were included in the top 50; the top mitochondrial gene (mAcon1) among them exhibited a betweenness centrality value of 3738 versus an average for the whole network of 486.12, which means that this gene may play a crucial role in maintaining the connectivity of the network and that, if it were removed, it would significantly disrupt the organization of the network. Instead, no mitochondrial genes were within the top 50 in terms of closeness, which in a network means that it may take longer for information to flow from that node to other nodes or, in a co-expression network, that they tend to cluster together and are less connected than nuclear genes; however, the top two mitochondrial genes as for closeness, i.e., Idh3b and mAcon1, were, respectively, 0.5 and 0.7 far from the top 50. As the last centrality measure, we focused on the clustering coefficient; seven mitochondrial genes, i.e., Cchl (Cytochrome c heme lyase), SdhB (Succinate dehydrogenase, subunit B), ND-B17.2 (NADH dehydrogenase B17.2 subunit), CG1907, Hmgcl (3-Hydroxy-3-methylglutaryl-CoA lyase), ND-20 (NADH dehydrogenase 20 kDa subunit), and CG1673, were among the 56 genes with the maximum score, i.e., clustering coefficient = 1.