# A Distributed Hybrid Community Detection Methodology for Social Networks
## 4 Experiments  
To assess the proposed methodology, both its execution characteristics along with the quality of the generated community structures are compared, in terms of objectivity, against the NetworkX's implementations of the Girvan-Newman's [8; 36] and the Clauset-Newman-Moore [1; 37] algorithms that generally serve as standards in the divisive community detection case. Thus, the overall performance for each the aforementioned approaches was contrasted on the thoroughly analyzed social graphs shown in Table 1.  
At this point, it should be emphasized that the over-demanding Girvan-Newman [36] and Clauset-Newman-Moore [37] NetworkX implementations has set strong hardware restrictions, limiting thusly the experimentation process to merely small social networks. All the experiments were conducted in an eight node Spark 2.3.2 cluster, with 4 GBs of RAM and two virtual cores per node. The execution parameters for which the proposed methodology had the best community performance [43] are shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **\# of Nodes** & **\# of Edges** & **Average Node Degree** \\ \hline Hamsterster [38] & 1858 & 12,534 & 13.49 \\ Openflights [39] & 2939 & 15,677 & 10.67 \\ Quakers [40] & 119 & 174 & 2.93 \\ Google + [41] \(-\) Egonet: & 1977 & 33,138 & 31.4733 \\
104226133029319075907 & & & \\ Google + [41] \(-\) Egonet: & 4609 & 69,545 & 31.7145 \\
112573107772208475213 & & & \\ Pokec [42] & 1,632,803 & 30,622,564 & 2.6292 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluated datasets. Even if it seems rather pointless to compare a classic implementation with one that is completely distributed and thus extremely scalable, as presented in Table 3, it should be highlighted that not only the execution time improvement percentage outreaches the 85% and 32% in the average case for the Girvan-Newman [8] and the Clauset-Newman-Moore [1] case, respectively, but also that as the number of edges of the analyzed social graph increases, the performance of the distributed proposed methodology is not proportionately affected. Additionally, in order to visually assess the generated community structures for each of the compared methods, the following graphical representations, Figures 2 and 3, show the returned community hierarchy structures for the Hamsterster and the Openflights information networks cases. As presented, in the aforementioned figures, the proposed methodology generates a much more segmented community structure comparing to the respective of the classic Girvan-Newman [8] and the Clauset-Newman-Moore [1] approaches. In other words, the proposed methodology tends to generate numerous, compact communities, while the classic approach find difficulties in dividing densely intra-connected but contextually unrelated network elements. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **LS-th Depth** & **EB-th Depth** & **LS Threshold** & **EB Threshold** & **NA Threshold** \\ \hline Hamsterster [38] & 3 & 3 & 70\% & 3 & 80\% \\ Openflights [39] & 4 & 4 & 70\% & 5 & 80\% \\ Quakers [40] & 4 & 4 & 70\% & 4 & 80\% \\ Google + [41] - Egonet: & 6 & 6 & 65\% & 9 & 70\% \\
104226133029319075907 & & & & & \\ Google + [41] - Egonet: & 6 & 6 & 65\% & 9 & 70\% \\
112573107772208475213 & & & & & \\ Pokec [42] & 8 & 8 & 50\% & 20 & 60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The proposed methodology best execution arguments. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Girvan–Newman [8]** & **Clauset–Newman–Moore [1]** & **Proposed Methodology** \\ \hline Hamsterster [38] & 843.34 & 174.53 & 134.8 \\ Openflights [39] & 5789.62 & 326.11 & 192.05 \\ Quakers [40] & 1.38 & 0.43 & 0.32 \\ Google + [41] - Egonet: & & 524.92 & 302.69 \\
10422613302931075907 & & & & \\ Google + [41] - Egonet: & & & & \\
112573107772208475213 & & & & \\ Pokec [42] & & & & \\ \hline \hline \end{tabular}
\end{table}