# A Distributed Hybrid Community Detection Methodology for Social Networks
## 4 Experiments

Table 3: The average required execution time (in seconds) per dataset and community detection method applied after 20 executions. Figure 2: The graphical comparison of the different generated community structures for the Hamsterster social graph per each method applied: (**a**) The Hamsterster original graph visualization; (**b**) the Girvan–Newman generated community structure; (**c**) the Clauset–Newman–Moore generated community structure; and (**d**) the hybrid proposed methodology returned community structure. Specifically, regarding the Openflights information network [39], where along with the name of each \"country\" involved, the geographic coordinates where also considered as part of the node attributes information, the consistency of the attribute relativeness is strongly assured. Since, after thoroughly analyzing the \"country\" node attribute distribution for the three largest communities returned per each community detection algorithm applied, as presented in Figure 4, the proposed methodology returned communities that not only have surprisingly relevant user content characteristics but also are in the truly correct order regarding the total number of flights. In particular, the first community is the one that groups the flights of the \"United States\", \"Mexico\", \"Canada\", \"Virgin Islands\", and \"Saint Lucia\" to the truly largest community, then the flights to \"China\" and \"Hong Kong\" are correctly grouped together and finally all the flights from \"Brazil\" form the truly third largest flights community. On the contrary, both Girvan-Newman [8] and Clauset-Newman-Moore [1] algorithms outcome unrelated, in terms of social context information, communities. This is a very critical conclusion, since due to the homophily related assumption initially made, it is a mandatory community detection quality that the proposed methodology should be attributed with. Finally, two network topology measures can also cross-validate the efficiency of the proposed methodology's generated community structure, against the corresponding of the Girvan-Newman's [8] and the Clauset-Newman-Moore [1]. The average generated community density [44], and the average generated community performance [43], which is the ratio of the number of intra-community edges plus the community non-edges with the total number of potential edges. As shown in Table 4, the proposed methodology tend to generate communities of similar density with the respective of Girvan-Newman [8] and Clauset-Newman-Moore [1] in the average case. This practically proves that despite the fact that the proposed methodology generates a much more segmented community structure, it successfully retains all the intra-connection edges as the community detection's standards. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Girvan–Newman [8]** & \
\begin{tabular}{c} **Clauset–Newman–** \\ **Moore [1]** \\ \end{tabular} &
\begin{tabular}{c} **Proposed** \\ **Methodology** \\ \end{tabular} \\ \hline Hamstersterster [38] & 0.005 & 0.0058 & 0.0105 \\ Openflights [39] & 0.0046 & 0.0032 & 0.0036 \\ Quakers [40] & 0.04124 & 0.0243 & 0.1033 \\ Google + [41] - Egonet: & & 0.0156 & 0.0144 \\
104226133029319075907 & & & \\ Google + [41] - Egonet: & & 0.0068 & 0.0076 \\
112573107772208475213 & & & 0.0149 \\ Pokec [42] & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average generated community density [44]. Figure 3: The graphical comparison of the different generated community structures for the Openflights information network per each method applied: (**a**) The Openflights original graph visualization; (**b**) the Girvan–Newman generated community structure; (**c**) the Clauset–Newman–Moore generated community structure; and (**d**) the hybrid proposed methodology returned community structure. Finally, as shown in Table 5, the proposed methodology constantly manages to achieve slightly better community performance than the divisive community detection baselines.