# Comparison of Functional Connectivity Analysis Methods in Alzheimer's Disease
## 3 Functional Connectivity Analysis Methods
### Data-Driven Methods
#### 3.2.3 Graph Theory based Method (GT)  
The seed-based and ICA methods are similar in that they both aim to extract temporally coherent networks. On the other hand, graph-theoretical methods are more commonly employed to characterize functional connections across all nodes (regions) of the brain. Assessing the topology of the functional connectome, a significant loss was measured in the small-world organization of the functional brain network in AD [40]. A study employed graph theory to identify network hubs before using PET imaging to reveal that \(\beta\)-amyloid deposition was substantially higher in certain areas. They speculated that there might be an activity-dependent mechanism that causes the accumulation of \(\beta\)-amyloid in highly active areas, such as the hubs (synapse) [41].  
Graph theory is a mathematical technique capable of defining the characteristics of complicated systems concisely and modeling interrelationships (expressed by edges) between brain regions (expressed by nodes). Graph theory can expose the topological features of a complex network and assess the status of the brain network using metrics such as node degrees, clustering coefficient, typical path length, and correlations.  
Here, ADNI data have been used for the experiment to measure FC using the graph theory method. All functional and structural MRI scans used in this study were collected using 3-T Philips scanners. The Data Processing Assistant for Resting-State fMRI (DPARSF) toolbox and the SPM12 toolbox were used to preprocess the images. The brain is divided  
Figure 5: DMN and ICA components and Correlation matrices using ICA for NC and AD patients.  
into 90 different areas by the automated anatomical labeling (AAL) atlas. Averaging the signals of all voxels inside the region generated the representative signal of each node (Figure 6a). Using [PERSON]'s correlation coefficient (\(p\)), the brain network's edges were defined as FC between all pairs of AAL areas. A high \(p\)-value contains more graph edges, resulting in a denser graph by retaining the weaker connections, which correspond to less significant and noisier correlations. A small value of \(p\), on the other hand, may eliminate many edges from the graph, generating a disconnected graph that cannot be utilized in the calculation of the graph metrics.  
Once the graphs were constructed, we computed different graph metrics to describe the brain's functional state. To examine the characteristics of 90 AAL brain areas,  
Figure 6: (**a**) Brain Network graph where nodes denote the voxel/ROI across the brain and edges denotes their functional connections (**b**) Graph-based estimation of correlation matrices for NCs and AD patients. The correlation matrices demonstrate the weaker/absent correlation in AD patients compared to NC.  
three local nodal measures (degree, participation coefficient, and betweenness centrality) and one network small-wordless measure were calculated. Using the Brain Connectivity Toolbox, the graph measures were computed based on weighted adjacency matrices (Figure 6b).  
The brain's functional network was generated using the correlation between the resting-state fMRI signals from different brain areas (Figure 6). Graph theory-based metrics were used to assess the change in FC of the brain network caused by AD. The graph theory findings in AD are more consistent than those in seed-based and ICA methods, most likely because of methodological differences. Considering the variations in data type and analysis, graph theory looks to be a promising technique for analyzing FC in NCs and AD.