Community analysis algorithm proposed by Clauset, Newman, and Moore (CNM algorithm) finds community structure in social networks. Unfortunately, CNM algorithm does not scale well and its use is practically limited to networks whose sizes are up to 500,000 nodes. The paper identifies that this inefficiency is caused from merging communities in unbalanced manner. The paper introduces three kinds of metrics (consolidation ratio) to control the process of community analysis trying to balance the sizes of the communities being merged. Three flavors of CNM algorithms are built incorporating those metrics. The proposed techniques are tested using data sets obtained from existing social networking service that hosts 5.5 million users. All the methods exhibit dramatic improvement of execution efficiency in comparison with the original CNM algorithm and shows high scalability. The fastest method processes a network with 1 million nodes in 5 minutes and a network with 4 million nodes in 35 minutes, respectively. Another one processes a network with 500,000 nodes in 50 minutes (7 times faster than the original algorithm), finds community structures that has improved modularity, and scales to a network with 5.5 million.
['Ken Wakita', 'Toshiyuki Tsurumi']
Finding Community Structure in Mega-scale Social Networks