Background: Recent studies have shown the dynamic functional connectivity (FC) of the brain. Accordingly, new challenges have arisen for analyzing and interpreting this rich information. New method: We identified the patterns of coherent FC using a novel method in computational topology called the persistence vineyard. It has been developed to track the characteristic change of the network topology under data perturbations in a threshold-free manner. Results: We showed the relevance of this new approach by examining the dynamic FC in the resting and gaming stages of 26 healthy subjects. Our proposed method revealed stage and band-specific FC states that were topologically robust. Comparison with existing methods: While principal component analysis (PCA) estimated similar patterns to our FC states, it produced spurious connectivity due to its orthogonality assumption. Temporal variations of local and global network properties were examined with graph measures. However, unlike the persistence vineyard approach, their results were affected by the network density and its unknown topology. Conclusions: Unlike the existing methods, the persistence vineyard provided a more reliable and robust way to estimate FC states. Their extracted network topology changes showed patterns consistent with those of previous studies. Therefore, it may be a potentially powerful tool for studying the dynamic brain network. (C) 2016 Elsevier B.V. All rights reserved.