# Uncovering Hidden Community Structure in Multi-Layer Networks
## 6 Evaluation of Results and Comparison
### Experimental Results  
For several real-world networks from various domains, HCD identifies multiple layers of high modularity community structure. For our experiment, we applied a HCD method on each of the selected dataset graphs. The proposed HCD method identified multiple layers of communities (2, 3, or 4) in different graphs, and the results of the algorithms are shown below in Table 2. HCD not only identifies the layers with the hidden or weak structure that the other community detection algorithms usually ignore, but also improves the detection accuracy of the dominant layer as it can be observed through the average modularity scores in Figure 5; although there is only a slight difference, in some cases, it does matter.  
After getting the above results from experimenting with the HCD algorithm on different real-world network datasets, we compared the results with two algorithms: (1) Infomap [26], which is a community detection algorithm capable of achieving high-quality com- munities. This algorithm is based on the principle of information theory and defines the community from the coding perspective. It uses Huffman coding and community structure secondary coding to obtain the maximum compression ratio. In this way, the problem of community detection is remodeled into an optimiza  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Dataset** & **Communities in Layers** & **Modularity in Layers** \\ \hline Dolphins & \(4,8\) & 0.56, 0.54 \\ Enron Email & \(7,9\) & 0.60, 0.44 \\ Fb-Pages-Politician & \(29,74,32\) & 0.79, 0.74, 0.61 \\ Citeseer & \(35,75\) & 0.85, 0.75 \\ DBLP & \(203,330,152\) & 0.80, 0.75, 0.65 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of the detected layers in different graphs with HCD method.  
Figure 5: Results of improvements in modularity scores of different graphs in each iteration. The vertical axis shows the modularity values and the horizontal axis is for the number of iterations.  
Louvain algorithm [3], which is an unsupervised modularity optimization algorithm (does not require the input of the number of communities). This method treats each node as a separate community in the initial phase and gradually optimizes the modularity by expanding the size of each community. After repeated iterations, the Louvain algorithm can get a community partition with the largest modularity value. Both algorithms give promising results when it comes to simple community detection but the performance decreases when considered in terms of detecting hidden communities in networks, as both the algorithms are unable to detect hidden communities. The difference is clear in Figure 4; HCD performs better than the other two and shows a high value of modularity.  
Additionally, the reason behind implementing the improvement step i.e., step three of the algorithm, in this work is to clarify the structure of the detected communities. From the experiments, it has been observed that communities detected after Layer 1 are more hidden as compared to the ones detected in Layer 1. So the average modularity results of the detected layers after each iteration are improved by rectifying the layers. Moreover, we also figured out that the average modularity scores of the layers detected on the actual network are greatly upgraded by making improvements in the layers. As an example, Figure 5 shows the increasing trend during the iterations when we detect two, three, or four community layers on five real-world networks.