Link community detection through global optimization and the inverse resolution limit of partition density

We investigate the possibility of global optimization-based overlapping community detection, using link community framework. We first show that partition density, the original quality function used in link community detection method, is not suitable as a quality function for global optimization because it prefers breaking communities into triangles except in highly limited conditions. We analytically derive those conditions and confirm it with computational results on direct optimization of various synthetic and real-world networks. To overcome this limitation, we propose alternative approaches combining the weighted line graph transformation and existing quality functions for node-based communities. We suggest a new line graph weighting scheme, a normalized Jaccard index. Computational results show that community detection using the weighted line graphs generated with the normalized Jaccard index leads to a more accurate community structure.