Assessing the impact of the density and sparsity of the network on community detection using a Gaussian mixture random partition graph generator.

Identification of sub-networks within a network is essential to understand the functionality of a network. This process is called as 'Community detection'. There are various existing community detection algorithms, and the performance of these algorithms can be varied based on the network structure. In this paper, we introduce a novel random graph generator using a mixture of Gaussian distributions. The community sizes of the generated network depend on the given Gaussian distributions. We then develop simulation studies to understand the impact of density and sparsity of the network on community detection. We use Infomap, Label propagation, Spinglass, and Louvain algorithms to detect communities. The similarity between true communities and detected communities is evaluated using Adjusted Rand Index, Adjusted Mutual Information, and Normalized Mutual Information similarity scores. We also develop a method to generate heatmaps to compare those similarity score values. The results indicate that the Louvain algorithm has the highest capacity to detect perfect communities while Label Propagation has the lowest capacity.