Network topology analysis

Network topology analysis was performed to measure properties of the regulatory systems. In graph theory, typically a network is a mathematical object that contains V vertices, E edges and/or A arcs. Node degree is the number of edges or linkages of each node. High-degree nodes, hub nodes, are important in a network since they have high relationships with others in the system. The shortest path length represents the shortest distance between any pairs of nodes, while the average path length is the average of all shortest paths between all possible pairs of nodes. The network diameter is the longest of the shortest paths between all pairs of nodes in a network. Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes in a network. It ranges between 0 and 1, which respectively quantifies low and high probabilities of the involvement a gene in gene–gene cooperation. Therefore, nodes with high betweenness centrality act as a linkage between neighbor genes in the network, facilitating gene–gene association. Local clustering coefficient is a measure of how neighboring nodes are connected to each other. It is computed for each node in the network, and the average of all local clustering coefficients represents the global clustering coefficient of the network. This parameter ranges from 0 to 1, indicating zero to complete connection between neighboring gene nodes of interest, respectively. All networks in this work were topologically analyzed using NetworkAnalyzer. The frequency of network motifs was computed using NetworkMotifDiscovery, and the network was visualized in Cytoscape3.6⁶⁴. Wilcoxon rank-sum test was used for statistical analysis of the topological parameters at p-value < 0.05. The random networks with equal numbers of nodes and edges used for the topological analysis were generated by Randomizer⁶⁵.