# Optimal Disintegration Strategy in Multiplex Networks under Layer Node-Based Attack
## 3 Experimental Analysis
### Experiments in Real Networks  
There is a large difference between the model networks and real systems in the edge connection and interlayer degree correlation. Therefore, in this section, we introduce some real multiplex networks for experiments. 1. _Caenorhabditis elegans_ connectome, where the multiplex consists of layers corresponding to different synaptic junctions: electric (Electric), chemical monadic (Chem. Mon), and polyadic (Chem. Pol). We use different pairs of layers to construct multiplex networks and obtain three different duplex networks. 2. _Drosophila melanogaster_ genetic and protein interaction network, where the multiplex consists of layers corresponding to different types of genetic interactions for organisms: direct interaction (Direct), suppressive genetic interaction (Supp. Gen) and additive genetic interaction (Add. Gen). We similarly use different pairs of layers to construct multiplex networks. 3. Top Noordin network, where the multiplex consists of three layers corresponding to different relationships among extremists active in Indonesia: trust (T), operations (O) and communication (C). More information about these networks is given in Table 1.  
The results of the six duplex networks under different disintegration strategies are given in Figures 4 and 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Network** & **Layers** & \(N\) & \(E^{[A]}\) & \(E^{[1]}\) & \(E^{[2]}\) & \(E^{[3]}\) \\ \hline \multirow{3}{*}{Caenorhabditis Elegans} & Electric - Chem. Mon. & 238 & 1833 & 1576 & 887 & / \\  & Electric-Chem. Pol & 252 & 1147 & 485 & 773 & / \\  & Chem. Mon.-Chem. Pol & 259 & 1804 & 511 & 1455 & / \\ \hline \multirow{3}{*}{Drosophila Melanogaster} & Direct - Supp. Gen. & 676 & 1946 & 668 & 1344 & / \\  & Direct-Add. Gen. & 625 & 1498 & 523 & 1024 & / \\ \cline{1-1}  & Supp. Gen.-Add. Gen. & 557 & 2117 & 1421 & 1164 & / \\ \hline Top Noordin Extermist & T-O-C & 79 & 620 & 259 & 437 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The basic information of the real multiplex networks. The first column represents the names of the different multiplex networks and the second column identifies the names of different layers used to construct multiplex networks. The other columns contain information about the number of nodes \(N\), the total number of edges in the aggregated network of each multiplex network \(E^{[A]}\) and the number of edges in each layer (\(E^{[1]}\), \(E^{[2]}\) and \(E^{[3]}\)). Figure 3: Optimal disintegration strategies in coupled ER networks with different degree correlation under layer node-based attack. The two layers are obtained independently with probability \(p=0.006\) and size \(N=500\). The two layers are coupled with there correlated structure (MN, UC and MP), in figures (**a**–**c**) respectively. We determine the mean value of \(\Phi\) over 20 independent realizations. Some conclusions obtained from Figure 3 are also shown in Figures 4 and 5. The performance of HLDA and CI strategies are generally better than the other strategies and close to that of optimal strategy when the network is close to collapse. Differently, for multiplex networks with a higher average degree in Figure 4, the performance of the layer node-based strategies is better than that of multiplex node-based strategies when the percentage of node removed is small (less than 0.2) and the optimal strategies have more advantages than other existing strategies. However, for the relatively sparse multiplex networks in Figure 5, some layer node-based strategies have similar performance with the optimal strategies and general advantage through multiplex node-based strategies in different attack length. We further experiment in the top Noordin extremist multiplex network with three layers.