On the detectability of node grouping in networks

In typical studies of node grouping detection, the grouping is presumed to have a certain type of correlation with the network structure (e.g., densely connected groups of nodes that are loosely connected in between). People have defined different fitness measures (modularity, conductance, etc.) to quantify such correlation, and group the nodes by optimizing a certain fitness measure. However, a particular grouping with desired semantics, as the target of the detection, is not promised to be detectable by each measure. We study a fundamental problem in the process of node grouping discovery: Given a particular grouping in a network, whether and to what extent it can be discovered with a given fitness measure. We propose two approaches of testing the detectability, namely ranking-based and correlation-based randomization tests. Our methods are evaluated on both synthetic and real datasets, which shows the proposed methods can effectively predict the detectability of groupings of various types, and support explorative process of node grouping discovery.