Tracking modularity in citation networks

Citation network analysis is an effective tool to analyze the structure of scientific research. Clustering is often used to visualize scientific domain and to detect emerging research front there. While we often set arbitrarily clustering threshold, there is few guide to set appropriate threshold. This study analyzed basic process how clustering of citation network proceeds by tracking size and modularity change during clustering. We found that there are three stages in clustering of citation networks and it is universal across our case studies. In the first stage, core clusters in the domain are formed. In the second stage, peripheral clusters are formed, while core clusters continue to grow. In the third stage, core clusters grow again. We found the minimum corpus size around one hundred assuring the clustering. When the corpus size is less than one hundred, clustered network structure tends to be more random. In addition even for the corpus whose size is larger than it, the clustering quality for some clusters formed in the later stage is low. These results give a fundamental guidance to the user of citation network analysis.