A new metric to compare local community detection algorithms in social networks using geodesic distance

Community detection problem is a well-studied problem in social networks. One major question to this problem is how to evaluate different community detection algorithms. This issue is even more challenging in the problem of local community detection where only local information of communities is available. Normally, two community detection algorithms are compared by evaluating their resulted communities. In this regard, the most widely used technique to evaluate the quality of communities is to compare them with the ground-truth communities. However, for a large number of networks, the ground-truth communities are not known. As a result, it is necessary to have a comprehensive metric to evaluate the quality of communities. In this study, improving a local quality metric, a number of local community detection algorithms are compared through assessing their detected communities. Furthermore, using some small graphs as example communities, some drawbacks of a number of existing local metrics are discussed. Finally, according to the experimental results, it is illustrated that the local community detection algorithms are fairly compared using the proposed metric, GDM. It is also shown that the judgment of GDM is almost the same as that of F1-score, i.e. the metric which compares the community with its ground-truth community.