# Temporal Label Walk for Community Detection and Tracking in Temporal Network
## 3 Experiment and Analysis
### Community Detection and Tracking  
This section we evaluate our method by real data sets. Firstly, different clustering methods are tested on _Students_, and then the results of TLW and other static community detection algorithms are given. Finally, we visualize our division result of _Students_ and _Facebook_. To evaluate results of different clustering methods based on (6), we use Students data set from 16:06:47 on 27 June 2014 to 23:58:51 on 27 June 2014 with 113 edges and 87 nodes. Figure 2 is the snapshot of the associated temporal network by mixing all edges together. Some obvious clusters can be observed around nodes 3 and 1713. Let the \(c=1\times 10^{-6}\) and \(\beta=1,\alpha=1\). Compute label values of nodes at 23:58:51, and use clustering analysis methods to reveal nodes in same community. Since the number of communities is unknown, we group the nodes by AP and DBSCAN, respectively. According to the results of AP and DBSCAN, setting the number of clusters to be 21, we also use Mini Batch K-means to cluster. Focusing on two key nodes 3 and 1713, Figure 6 shows the results of community detection. According to the division of \(X_{u}(t)\), community structure is in accordance with the actual situation and dependence on clustering algorithms is not strong. The modularity and running time of three methods are listed in Table 1.  
Figure 5: Label value of node 3 with non-normalization and normalization. The value increases exponentially without normalization (see (**a**)), but tends to be stable after normalization (see (**b**)). Figure 6: Results of community detection with AP, Mini Batch K-means, and DBSCAN. The blue nodes and node 3 are in the same community. The orange nodes belong to community of node 1713. The division is only different in a few points. It is shown that modularity greater than about 0.3 appear to indicate significant community structure in practice [24], and typically fall in the range from 0.3 to 0.7 [1]. According to Table 1, we find that all three methods can get a good community structure with reasonable modularity, but AP is obviously more computational expensive than Mini Batch K-means and DBSCAN, which may make AP impractical in processing large-scale networks. Compared with other two methods, Mini Batch K-means gets better community structure and runs faster with the increase of data. If the community structure is stable in a certain period, DBSCAN method can be used firstly and then Mini Batch K-means can be used to approximate it. Mini Bath K-means is used in subsequent experiments. We choose node 525 (see Figure 6) to track the community evolution based on label value, the result is shown in Figure 7. Node 525 joins the community halfway, and does not interact directly with 1713. The number of communities in this experiment is set to 21 for a network with 87 nodes. It may be too many for a real social network. One reason is that some nodes communicate little with other nodes, which makes them become noise points in clustering analysis. In the case of large-scale data sets, noise points are often categorized separately because of inadequate information of time. To evaluate our method in community detection, we compare modularity with other static community detection algorithms. We choose partial community detection methods that focus on static graph: K-clique [25], asynchronous label propagation [26] and label propagation [3]. The dynamic community detection algorithm of [6] called DABP is also included. Data streams on 27 June are mixed to an undirected snapshot with 87 nodes and 85 edges. The result is shown in Table 2. All methods have a good performance with high modularity on the first day. Please note that our method is to reveal the community structure at 23:58:51. With the passing of time, Figure 8 shows the change of modularity of all methods. Here modularity of all methods decreases with the increase of time.