*4.4. Community Detection in the Cryptocurrency Market*

Given a MST from the distance matrix **D**, different communities are formed and can be recognized clearly, i.e., cryptocurrencies belonging to one community have short distance edges among them and the distance between two others in two different communities is longer than any edges of these two communities. However, there are less common cases in which some nodes are scattered between communities, or it is not visible from the graph how close the two communities are. This issue motivates us to further analyze the MST to optimize the clustering result using several community detection methods which have been developed [99–103]. Of these, the Louvain method is applicable across a wide range of domains [104–107]. Thus, we apply this method to our MST in order to obtain optimal communities. Theoretically, Louvain is an optimization problem that uses *Modularity* to measure the density of links inside communities compared to links between communities. The target of Louvain is to minimize the Modularity measure, which means that different authentic communities are clustered very tightly [108].

However, it is not convincing just to show results from one method only, as the community structure of a network might be just random. To overcome this issue, we also adopt another commonly used method named Girvan–Newman, which removes edges from the original graph one-by-one such that the edge having the highest number of shortest paths between nodes passing through it is removed first. Eventually, the graph breaks down into smaller pieces, so-called communities [109].

If the results proposed by these two community detection methods are similar, it implies that the relationship of the cryptocurrencies as well as their corresponding community structure are reliable and reflects their genuine characteristics. The results after applying these methods are shown in Section 5.
