Due to its relatively few assumptions, independent component analysis (ICA) has become a widely-used tool for the analysis of functional magnetic resonance imaging (fMRI) data. In its application, Infomax, has been by far the most frequently used ICA algorithm, primarily because it is the first ICA algorithm applied to fMRI analysis. However, now there are a number of more flexible ICA algorithms, which can exploit multiple types of statistical properties of the signals with fewer assumptions. In this work, we investigate the performance of Infomax and two of the more recent ICA algorithms, entropy bound minimization (EBM) and entropy rate bound minimization (ERBM), on resting state fMRI data derived from a large number of patients with schizophrenia (SZs) and healthy controls (HCs). In order to overcome the difficulty of directly comparing the performances of different ICA algorithms on real fMRI data, we propose the use of graph theoretic (GT) metrics to assess the quality of an ICA decomposition by measuring an algorithm's ability to capture the inherent differences between SZs and HCs. Our results show that ERBM, the algorithm which incorporates the greatest number of statistical properties of the signals, provides the best performance for fMRI analysis.