# Distributed Centrality Analysis of Social Network Data Using MapReduce
## 2 Methods
### Data Collection
The method used for calculating closeness centrality is therefore ineffective for the Twitter network, as it contains many disconnected nodes. Several other approaches can be worked out by taking the disconnected nodes into consideration. Figure 4: Summary of the number of nodes and edges in the Twitter dataset. The distributed approach implemented and described in this paper was compared with the conventional approach, that is, the one implemented without using parallel processing methods. Figure 6 presents the performance improvement obtained through the MapReduce approach for various centrality measures within the network collected on the first day, second day, and third day, respectively. In the first day of data, the average improvement through a distributed approach was 32.30% for the computation of degree centrality. The average speed-up for the computation of closeness centrality in the distributed approach was 22.81%, while it was 36.64% for the computation of eigenvector centrality. In the second day of data, the average speed up in using a distributed approach was 33.05% for the computation of degree centrality. The average improvement for the computation of closeness centrality in the distributed approach was 47.27%, whereas it was 51.32% for the computation of eigenvector centrality. In the third day of data, the average speed-up in using a distributed approach was 54.15% for the computation of degree centrality. The average speed-up for the computation of closeness centrality in a distributed approach was 51.95%, while it was 35.46% for the computation of eigenvector centrality. Summarizing, the proposed MapReduce based approach improved the performance of calculation of degree centrality by 39.8%, closeness centrality by 40.7%, and eigenvalue centrality by 41.1%. Note that using MapReduce for centrality calculation lead to an improvement in execution time. In other systems, breadth first search (BFS) is used in the calculation of the distances between nodes in closeness centrality, and the time complexity of BFS is \(\theta\big{(}n^{2}\big{)}\), where \(n\) is the number of network nodes. However, in the distributed approach, complexity is reduced to \(\theta(dn)\), where \(d\) refers to the diameter of the graph and possess constant value. The value of \(d\) is often much smaller than the total number of network nodes. Figure 5: Top 10 central nodes under different centrality measures for day III in the Twitter dataset. ## 4 Conclusions

To calculate network centrality measures, we proposed a distributed framework based on a MapReduce computation model, along with the Hadoop distributed file system (HDFS) as the storage platform. The breadth first search (BFS) algorithm was implemented in a distributed manner to collect local and global information around each node, which was then used to calculate degree and closeness centrality. We have calculated centrality measures for top 10 central nodes of a dynamic Twitter network. The comparison between the distributed and conventional approaches showed that the performance of the distributed approach was better (on average, 39.8%, for degree centrality, 40.7% for closeness centrality, and 41.1% for eigenvector centrality). This empirical study demonstrated that the proposed distributed approach is scalable and helps in efficient computation and pattern recognition of large-scale social network datasets, such as the Twitter dataset. Conceptualization, R.K.B. and S.K.R. ; Investigation, S.M. ; Methodology, R.K.B. and S.K.R. ; Software, R.K.B. and S.K.R. ; Supervision, S.M. ; Validation, R.K.B., S.K.R. and S.M. ; Visualization, R.D. ; Writing--original draft, R.K.B. and S.K.R. ; Writing--review & editing, R.D. and R.M. This research received no external funding. The authors declare no conflict of interest. ## References

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