Functional connectivity (FC) has become a leading method for resting-state functional magnetic resonance imaging (rs-fMRI) analysis. However, the majority of the previous studies utilized pairwise, temporal synchronization-based FC. Recently, high-order FC (HOFC) methods were proposed with the idea of computing "correlation of correlations" to capture high-level, more complex associations among the brain regions. There are two types of HOFC. The first type is topographical profile similarity-based HOFC (tHOFC) and its variant, associated HOFC (aHOFC), for capturing different levels of HOFC. Instead of measuring the similarity of the original rs-fMRI signals with the traditional FC (low-order FC, or LOFC), tHOFC measures the similarity of LOFC profiles (i.e., a set of LOFC values between a region and all other regions) between each pair of brain regions. The second type is dynamics-based HOFC (dHOFC) which defines the quadruple relationship among every four brain regions by first calculating two pairwise dynamic LOFC "time series" and then measuring their temporal synchronization (i.e., temporal correlation of the LOFC fluctuations, not the BOLD fluctuations). Applications have shown the superiority of HOFC in both disease biomarker detection and individualized diagnosis than LOFC. However, no study has been carried out for the assessment of test-retest reliability of different HOFC metrics. In this paper, we systematically evaluate the reliability of the two types of HOFC methods using test-retest rs-fMRI data from 25 (12 females, age 24.48 ± 2.55 years) young healthy adults with seven repeated scans (with interval = 3-8 days). We found that all HOFC metrics have satisfactory reliability, specifically (1) fair-to-good for tHOFC and aHOFC, and (2) fair-to-moderate for dHOFC with relatively strong connectivity strength. We further give an in-depth analysis of the biological meanings of each HOFC metric and highlight their differences compared to the LOFC from the aspects of cross-level information exchanges, within-/between-network connectivity, and modulatory connectivity. In addition, how the dynamic analysis parameter (i.e., sliding window length) affects dHOFC reliability is also investigated. Our study reveals unique functional associations characterized by the HOFC metrics. Guidance and recommendations for future applications and clinical research using HOFC are provided. This study has made a further step toward unveiling more complex human brain connectome.