# Large Scale Community Detection Using a Small World Model
## 7 Experimental Results
The evaluation metrics such as min-value, max-value, upper (25%), middle (50%) and lower (75%) quartile values have been listed in Table 3. \(NMI\) value provided by the CDSW algorithm at each point in the box plot is observed to be better. It may be observed that the Walktrap algorithm performs close to the proposed algorithm with respect to the \(NMI\) metric. Modularity metric indicates the quality of community partition. A \(t\)-test has been performed for static analysis of all mentioned community detection algorithms. Mean deviation and \(p\)-value have been extracted from the \(t\)-test. The mean deviation of evaluation metrics for all the algorithms are presented in Table 4. It may be noticed from Table 4 that the CDSW algorithm has positive deviation for all evaluation metrics, and it implies that it performs better with respect to all metrics. \(p\)-value in the \(t\)-test represents a significant difference of the CDSW algorithm with respect to other algorithms. Table 5 lists the statistics of \(p\)-value between all algorithms. An algorithm is said to be significantly different from others if its \(p\)-value is less than 0.05. It can be further noticed from Table 5, that \(p\)-value for the proposed algorithm in all of the evaluation metrics is less than 0.05. From this observation, it may be inferred that the CDSW algorithm is significantly different from all other algorithms with respect to metrics considered for comparison. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Modularity**} & \multicolumn{4}{c}{\(NMI\)} & \multicolumn{4}{c}{**F-Measure**} \\ \hline  & **INF** & **SG** & **GN** & **WT** & **CDSW** & **INF** & **SG** & **GN** & **WT** & **CDSW** & **INF** & **SG** & **GN** & **WT** & **CDSW** \\ \hline INF & 0.000 & \(-0.010\) & \(-0.002\) & \(-0.028\) & \(-0.042\) & \(0.000\) & \(-0.010\) & \(-0.002\) & \(0.028\) & \(-0.042\) & \(0.000\) & \(-0.005\) & \(-0.006\) & \(-0.009\) & \(-0.036\) \\ SG & 0.010 & 0.000 & \(0.008\) & \(-0.018\) & \(-0.032\) & \(0.010\) & \(0.000\) & \(0.008\) & \(-0.018\) & \(-0.032\) & \(0.005\) & \(0.000\) & \(-0.001\) & \(-0.003\) & \(-0.030\) \\ GN & 0.002 & \(-0.008\) & 0.000 & \(-0.002\) & \(-0.040\) & \(0.002\) & \(-0.008\) & \(0.000\) & \(-0.002\) & \(-0.040\) & \(0.006\) & \(0.001\) & \(0.000\) & \(-0.003\) & \(-0.029\) \\ WT & 0.028 & 0.018 & 0.026 & 0.000 & \(-0.014\) & 0.028 & 0.018 & 0.026 & 0.000 & \(-0.014\) & \(0.009\) & \(0.003\) & \(0.003\) & \(0.000\) & \(-0.027\) \\ CDSW & 0.042 & 0.032 & 0.040 & 0.014 & 0.000 & 0.042 & 0.032 & 0.040 & 0.014 & 0.000 & 0.036 & 0.030 & 0.029 & 0.027 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean deviation in modularity, \(NMI\) and F-measure for different algorithms. Figure 4: Comparative analysis of execution time (s) for synthetic datasets. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Modularity**} & \multicolumn{4}{c}{\(NMI\)} & \multicolumn{4}{c}{**F-Measure**} \\ \hline  & **MIN** & **25\%** & **50\%** & **75\%** & **MAX** & **MIN** & **25\%** & **50\%** & **75\%** & **MAX** & **MIN** & **25\%** & **50\%** & **75\%** & **MAX** \\ \hline INF & 0.46 & 0.59 & 0.73 & 0.81 & 0.86 & 0.54 & 0.68 & 0.75 & 0.81 & 0.92 & 0.57 & 0.72 & 0.76 & 0.83 & 0.93 \\ SG & 0.46 & 0.6 & 0.72 & 0.79 & 0.83 & 0.58 & 0.7 & 0.76 & 0.82 & 0.93 & 0.58 & 0.72 & 0.78 & 0.85 & 0.92 \\ GN & 0.43 & 0.59 & 0.68 & 0.77 & 0.85 & 0.58 & 0.69 & 0.75 & 0.81 & 0.88 & 0.54 & 0.74 & 0.78 & 0.8