**2. Methodological Overview of Resting-State fMRI (rs-fMRI) Studies**

Various analytical strategies are available to study resting-state network connectivity [59]. (1) Seed-based analysis is a hypothesis-driven approach when researchers initially select the seed region of interest based on their hypothesis and a calculated brain connec-

tivity map by detecting temporal correlation [48]. Seed-based analyses are attractive for assessing FC changes in small samples with good statistical power; however, whole-brain analyses are required to address a more comprehensive understandings on changes in rs-fMRI [60]. (2) Regional homogeneity (ReHo) evaluates the similarity or synchronization between different time series given a region or given regions and their neighbors [61]. (3) Independent component analysis (ICA) is a more complex approach that decomposes the whole brain into a set of independent components as a functional map [62,63]. (4) Graph theory constructs models of interrelationships (represented by edges) between brain regions (represented by nodes) and assesses the state of the brain network using various measures [64,65]. (5) To address directional interaction within and between functional networks, incorporating resting-state effective connectivity have been conducted [66]. Data-driven techniques such as Granger causal analysis and Bayesian network analysis provide new insights into effective connectivity [66,67]. (6) The amplitude of low-frequency fluctuation (ALFF) and fractional ALFF (fALFF) techniques were developed to assess the spontaneous low frequency (0.01–0.08 Hz) fluctuations in the fMRI signal intensity at rest, which could reflect the intensity of regional brain spontaneous neural activity [68,69].

Several rs-fMRI studies, aiming to unravel the neurobiological mechanisms of depression and dementia, have investigated abnormalities in various structures, including the frontal gyrus, precuneus, cingulate gyrus, parahippocampal cortex, cerebellum, or putamen [70–72]. However, recent meta-analyses of these studies did not reveal any significant regional convergence of neuroimaging findings for depression [73,74], suggesting that no single brain region is exclusively responsible for LLD's heterogeneous symptoms. A behavior or a clinical symptom typically involves synchronizing many brain regions in a network-based fashion [75]. Experiments have identified three major functional networks in LLD, AD, and MCI: (1) the default mode network (DMN), (2) executive control network (ECN), and (3) salience network (SN) [41,76–78]. Below, we review rs-fMRI studies in LLD, AD, and MCI patients according to individual neural networks for ease of interpretation of the results associated with cognitive function. The analysis methods for resting-state functional connectivity, reference anatomy used for brain parcellation, types of scanners, and characteristics of groups included in the study are essential pieces of information to understand the study results clearly. Therefore, we presented the table which summarizes sample size, age, study type, scanner type, reference space, and analysis method of each section's key studies in Supplementary materials.

## **3. The Default Mode Network (DMN)**
