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.
One of the first comparative studies is reported in @cite_45 . Four real-world networks with size up to three hundred thousand nodes are used in order to analyze the outputs of five algorithms. In this work, as the ground-truth community structure is not known, eleven quality metrics are investigated. Only two overlapping community detection algorithms are considered. First of all, it appears that the algorithms optimize the quality metrics over a range of size scales. Additionally, many quality metrics favors small clusters. Optimization of the quality metrics in the detection algorithms introduces a systematic bias into the extracted clusters. Indeed, a small variation of the quality scores can lead to great variability in the community structure. This work suggests that the link between quality metrics and the community structure is relatively loose.
@cite_45
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Detecting clusters or communities in large real-world graphs such as large social or information networks is a problem of considerable interest. In practice, one typically chooses an objective function that captures the intuition of a network cluster as set of nodes with better internal connectivity than external connectivity, and then one applies approximation algorithms or heuristics to extract sets of nodes that are related to the objective function and that "look like" good communities for the application of interest. In this paper, we explore a range of network community detection methods in order to compare them and to understand their relative performance and the systematic biases in the clusters they identify. We evaluate several common objective functions that are used to formalize the notion of a network community, and we examine several different classes of approximation algorithms that aim to optimize such objective functions. In addition, rather than simply fixing an objective and asking for an approximation to the best cluster of any size, we consider a size-resolved version of the optimization problem. Considering community quality as a function of its size provides a much finer lens with which to examine community detection algorithms, since objective functions and approximation algorithms often have non-obvious size-dependent behavior.