# Large Scale Community Detection Using a Small World Model
## 9 Conclusions  
The community detection problem is one of the challenging ones in social network analysis. In this study, communities have been detected in a distributed manner in order to have lesser computation time. Large-scale networks always follow small world phenomenon, which is based on the six degrees of separation principle. In this paper, similarity value between every pair of nodes has been obtained based on the random walk up to 3 rd walk length. From the experimental analysis, it is observed that the proposed algorithm i.e., CDSW, provides better performance based on values of modularity, NMI and F-measure as compared to a few other community detection algorithms referred to in literature. From \(t\)-test analysis, the proposed algorithm is observed to be significantly different from other algorithms. It also provides better performance in terms of execution time, especially when large-scale networks are considered.  
For the sake of simplicity, we have implemented all the algorithms in the undirected network. However, the proposed algorithm can be extended to the directed network by carefully choosing the source node in the network. As the network is a directed one, the source node can't be chosen randomly. The node with only the in-degree feature cannot be the source node for further processing. By imposing a constraint on choosing criteria for source node (i.e., source node must have at least one out-degree), the proposed algorithm can be extended to detect community for the directed network.  
The proposed algorithm can be further extended to dynamic social networks, where a large number of nodes along with their relationships are added more frequently. In future, other distributed frameworks like Spark and Storm may be implemented in the community detection process, in order to have further improvement in execution time.  
**Acknowledgments:** Thanks to the authorities of the NIT, Rourkela for availing the platform for doing this research study. Support also came from Covenant University Centre for Research and Innovation Development, Ota, Nigeria; and Research Cluster Fund of Faculty of Informatics, Kaunas University of Technology, Kaunas, Lithuania. All authors discussed the contents of the manuscript and contributed to its preparation. [PERSON] supervised the research. [PERSON] contributed the idea, performed the numerical simulations. [PERSON], [PERSON] and [PERSON] helped in the analysis of the framework developed and the writing of the manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\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}{_NM1_} & \multicolumn{4}{c}{**F-Measure**} \\ \hline  & **INF** & **SG** & **GN** & **WT** & **CDSW** & **INF** & **SG** & **GN** & **WT** & **CDSW** & **INF** & **SG** & **GN** & **WT** & **CDSW** \\ \hline INF & - & 0.241 & 0.761 & 0.001 & 0.000 & - & 0.241 & 0.761 & 0.001 & 0.000 & - & 0.324 & 0.442 & 0.234 & 0.000 \\ SG & 0.241 & - & 0.203 & 0.008 & 0.000 & 0.241 & - & 0.203 & 0.008 & 0.000 & 0.324 & - & 0.875 & 0.562 & 0.000 \\ GN & 0.761 & 0.203 & - & 0.000 & 0.000 & 0.761 & 0.203 & - & 0.000 & 0.000 & 0.442 & 0.875 & - & 0.515 & 0.000 \\ WT & 0.001 & 0.008 & 0.000 & - & 0.015 & 0.001 & 0.008 & 0.000 & - & 0.015 & 0.234 & 0.562 & 0.515 & - & 0.000 \\ CDSW & 0.000 & 0.000 & 0.000 & 0.015 & - & 0.000 & 0.000 & 0.000 & 0.015 & - & 0.000 & 0.000 & 0.000 & 0.000 & - \\ \hline \hline \end{tabular}
\end{table}
Table 5: \(p\)-value obtained from \(t\)-test for modularity, \(NM1\) and F-measure.