Specifically, the reliability of a fictitious co-authorship network at a given time t was analyzed taking into account, first, the reliability of nodes (researchers) equal and different, and, second, the reliability of edges (co-authorship relations), equal and different.
According to the configuration of the fictitious co-authorship network of Figure 1 and the relationships of the existing co-authorship, when the two situations for different rates of p (emphasis on edges and then emphasis on nodes) are compared, one may see that as p decreases, the reliability of the network becomes close to zero more quickly in the first case (edges or unreliable co-authorship relations) than in the second (nodes or unreliable researchers), as Figure 4 shows.
So that the reliability of the fictitious co-authorship network could be increased and the importance of centrality measures in this context could be introduced, within all possible insertion options of a new edge (or co-authorship relation) in graph G of Figure 1, nine non-isomorph graphs (1), described in Table 3, could be produced.