# On Edge Pruning of Communication Networks under an Age-of-Information Framework
## 8 Simulation
### Experimental Results
#### 8.2.2 The Low-Clustered Topology  
Now, we observe the simulation results of the low-clustered topology. Figures 12 and 13 too demonstrate the trade-off between the average AoI value and the number of duplicate messages received at the destination node \(d\) after the time until the first copy of the next message is received at the destination node. Again, the simulation is conducted by running the pruning algorithm multiple times and observing the critical area at which the trade-off settles at balance.  
In this case too, the total average AoI value increases in an exponential fashion as the number of links pruned from the network increases. This increase in the number of pruned links makes the network need more time to deliver the messages from node \(s\) to node \(d\) in a way that renders the received messages less fresh. On the other hand, pruning the messages reduces the number of paths between node \(s\) to node \(d\). This reduction in paths leads to reduce the number of duplicate messages received at the destination node \(d\).  
Figure 11: The simulation results from running the pruning algorithm on the high-clustered topology when \(\mu=2\). The left column is the result after running the algorithm when \(\sigma=1\) and the right column is the result after running the algorithm when \(\sigma=2\).  
Figure 10: The simulation results from running the pruning algorithm on the high-clustered topology when \(\mu=1\). The left column is the result after running the algorithm when \(\sigma=1\) and the right column is the result after running the algorithm when \(\sigma=2\).  
Figures 12 and 13 show that the correlation between the number of pruned links and the average AoI of the network is near the exponential in the low-cluster topology case, while the number of duplicate messages decreases in a more steep near-linear fashion compared with the reduction in the high-cluster case.  
We here too highlight the plots of the simulation to show a region of trade-off that achieves a relatively good reduction in the number of duplicate messages received at \(d\) and the total average AoI of the network. This highlighted area spawns the region of this empirical balance between AoI and message redundancy. We see again that the number of pruned links with relative to the total number of links in the network is within the same range shown in the high-clustered topology case.  
Furthermore, in this case, we see that the total average AoI becomes more sensitive to the number of pruned links as the value of the standard deviation \(\sigma\) increases. On the other  
Figure 12: The simulation results from running the pruning algorithm on the low-clustered topology when \(\mu=1\). The left column is the result after running the algorithm when \(\sigma=1\) and the right column is the result after running the algorithm when \(\sigma=2\).  
Figure 13: The simulation results from running the pruning algorithm on the low-clustered topology when \(\mu=2\). The left column is the result after running the algorithm when \(\sigma=1\) and the right column is the result after running the algorithm when \(\sigma=2\).  
hand, we see too that the number of duplicate messages after the significant time becomes more sensitive to the number of pruned links with high values of \(\sigma\). Regarding the effect of \(\mu\), we see that increasing its value increases the sensitivity of the change of the AoI and the number of duplicate messages too.