Is Objective Function the Silver Bullet? A Case Study of Community Detection Algorithms on Social Networks

Community detection or cluster detection in networks is a well-studied, albeit hard, problem. Given the scale and complexity of modern day social networks, detecting ``reasonable'' communities is an even harder problem. Since the first use of k-means algorithm in 1960s, many community detection algorithms have been invented - most of which are developed with specific goals in mind and the idea of detecting ``meaningful'' communities varies widely from one algorithm to another. With the increasing number of community detection algorithms, there has been an advent of a number of evaluation measures and objective functions such as modularity and internal density. In this paper we divide methods of measurements in to two categories, according to whether they rely on ground-truth or not. Our work is aiming to answer whether these general used objective functions are well consistent with the real performance of community detection algorithms across a number of homogeneous and heterogeneous networks. Seven representative algorithms are compared under various performance metrics, and on various real world social networks.