Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment of these algorithms is a thriving open question. If the ground-truth community structure is available, various clustering-based metrics are used in order to compare it versus the one discovered by these algorithms. However, these metrics defined at the node level are fairly insensitive to the variation of the overall community structure. To overcome these limitations, we propose to exploit the topological features of the 'community graphs' (where the nodes are the communities and the links represent their interactions) in order to evaluate the algorithms. To illustrate our methodology, we conduct a comprehensive analysis of overlapping community detection algorithms using a set of real-world networks with known a priori community structure. Results provide a better perception of their relative performance as compared to classical metrics. Moreover, they show that more emphasis should be put on the topology of the community structure. We also investigate the relationship between the topological properties of the community structure and the alternative evaluation measures (quality metrics and clustering metrics). It appears clearly that they present different views of the community structure and that they must be combined in order to evaluate the effectiveness of community detection algorithms.
This article reviews the state-of-the-art in overlapping community detection algorithms, quality measures, and benchmarks. A thorough comparison of different algorithms (a total of fourteen) is provided. In addition to community-level evaluation, we propose a framework for evaluating algorithms' ability to detect overlapping nodes, which helps to assess overdetection and underdetection. After considering community-level detection performance measured by normalized mutual information, the Omega index, and node-level detection performance measured by F-score, we reached the following conclusions. For low overlapping density networks, SLPA, OSLOM, Game, and COPRA offer better performance than the other tested algorithms. For networks with high overlapping density and high overlapping diversity, both SLPA and Game provide relatively stable performance. However, test results also suggest that the detection in such networks is still not yet fully resolved. A common feature observed by various algorithms in real-world networks is the relatively small fraction of overlapping nodes (typically less than 30p), each of which belongs to only 2 or 3 communities.