As a group-level statistic, reliability refers to the inter-individual or between-subject variability \( V_b \) relative to the intra-individual or within-subject variability \( V_w \). Both the intra- and inter-individual variances can be estimated using linear mixed model (LMM). In network neuroscience, given a functional graph metric \( \phi \), we considered a random sample of \( h \) subjects with \( n \) repeated measurements of a continuous variable. \( \phi_{ij} \) (for \( i=1, ..., n \) and \( j=1, ..., h\)) denotes the metric from the \( j^{th} \) subject's \( i^{th} \) measurement occasions. The two level LMM models \( \phi_{ij} \) as the following equations:

Where \( \gamma_{00} \) is a fixed parameter (the group mean) and \( s_{0j} \) and \( e_{ij} \) are independent random effects normally distributed with a mean of 0 and variances \( \sigma_{s0}^{2} \) and \( \sigma_{e}^{2} \). The term \( s_{0j} \) is the subject effect and \( e_{ij} \) is the measurement residual. Age, gender and interval(\( \Delta \mathrm{t} \)) can be covariant.