# Reliable Design for a Network of Networks with Inspiration from Brain Functional Networks
## 4 Evaluation
### Evaluation Results
#### 4.3.2 Designing Influencers on the PV-NoN Model  
In this section, we investigate the importance of influencer deployment regarding inter/intranetwork assortativity. Because we confirmed above that type-DD prevails over the other two types, we focus on type-DD in this evaluation to investigate how to improve the performance further. The simulation settings are basically the same as those described in the previous evaluation, and we again use the GCS and packet delay to evaluate the availability and communication performance, respectively. However, to show the results concisely, we set the arrival rate for both VNs to \(\lambda=0.5\) because the evaluation above confirmed that changes in performance can be seen with that value. As for the inter/intranetwork assortativity of network influencers, we picked three cases for each assortativity: (i) _assort_. is the case in which the rewiring procedure described in Section 4.1 is repeated until the connectivity converges with the highest assortativity, (ii) _disassort_. corresponds to the analogous case with the lowest _assort_. value, and (iii) _non-assort_. is the case in which the original connectivity pattern is maintained. Figure 6 shows to the GCS evaluation results, and Figure 7 shows those for the packet delay. First, we find that the GCS is increased when the intranetwork connectivity is assortative (i.e., \(\eta>0\)) and the internetwork connectivity is disassortative (i.e., \(\theta<0\)). We have shown previously that an assortative single network is fragile against random failures [47]. However, it is notable that the results in Figure 7 tell us the opposite. We assume that when each VN topology is assortative, the overlapping of the  
Figure 5: Variation of packet delay with arrival rate \(\lambda\). The vertical axis represents the packet delay, required time steps for a packet to be transmitted. Similarly to Figure 4, the solid lines in (**a**,**c**) correspond to the average packet delay of the two VNs, whereas the packet delays for each VN are plotted separately in (**b**,**d**). The horizontal axis represents the arrival rate \(\lambda\). In (**b**,**d**), note that \(\lambda\) is changed on VN1 but fixed on VN2. shared physical resources among the VNs becomes concentrated on a local area of the entire NoN, thereby enhancing the availability when each VN is formed assortatively. By contrast, when \(\theta<0\), the high-influence nodes are likely to not be shared among the VNs but rather to be dedicated to each VN. Consequently, an efficient resource utilization is realized, resulting in improved availability. The results also show that the assortativity configuration has greater influence on networks based on the BA model. Because of the biased degree distribution and the limitation in the procedure of topology construction, influencers have greater impact with the BA model. However, because the ER model (i) has a more uniform degree distribution compared to the BA model and (ii) its topological structure is generated randomly, the impact of the assortativity configuration is smaller. By contrast, Figure 7 shows that the packet-delay performance is increased when intranetwork connectivity is disassortative (i.e., \(\eta<0\)). When a network topology is formed assortatively, the network diameter becomes large and the communication performance degrades. It is true that assortative connectivity within each VN has a positive impact on availability, as seen in Figure 6. However, from a practical viewpoint of communication performance, we find that the increase of network diameter has a larger negative impact, resulting in degraded communication performance. As for the internetwork assortativity, the packet delay is decreased when it is disassortative, similar to the performance of GCS. We ran simulations on type-UD and type-SD as well, but these merely confirmed that they show almost the same tendency in relation to the inter/intranetwork assortativity.