Graph Theoretical Analysis of Functional Brain Networks in Neurodegenerative Disorders

Graph theory offers a mathematical framework to characterise the brain as a complex network of nodes, representing regions, connected by edges that mirror functional interactions. In neurodegenerative disorders such as Alzheimer’s disease, frontotemporal dementia and Parkinson’s disease, progressive synaptic dysfunction and neuronal loss disrupt the balance between local specialisation and global integration. Graph theoretical metrics—small-worldness, clustering coefficient, characteristic path length, network modularity and hub centrality—quantify network organisation, revealing a shift from efficient small-world topologies towards more random or overly segregated configurations. These alterations correlate with cognitive decline, reflect compensatory reorganisation in preclinical stages and identify vulnerable hub regions that accumulate pathology. Methodological advances in dependency estimation, thresholding and network construction have refined the detection of frequency-specific synchrony changes in both electroencephalography and magnetoencephalography. Emerging applications include non-invasive biomarkers for early diagnosis, monitoring disease progression, and targets for neuromodulation.

Research from Nature Portfolio

Systematic evaluation of functional network construction has demonstrated that choices in dependency estimation and binarisation exert a strong influence on topological measures. Comparative analyses using Pearson correlation, coherence, phase-order parameters and synchronisation likelihood, followed by binarisation via minimum spanning tree, minimum connected component and fixed thresholds, found that certain combinations—particularly coherence with a connectivity-preserving binarisation—enhanced the separation between Alzheimer’s patients and healthy controls. This work underscores the necessity of standardised pipelines to ensure reproducibility and to avoid contradictory findings that arise purely from methodological heterogeneity.

Graph Theoretical Analysis of Functional Brain Networks in Neurodegenerative Disorders publication trend

The graph below shows the total number of articles in graph theoretical analysis of functional brain networks in neurodegenerative disorders across all publications each year (not limited to Nature Index journals).

Technical terms

Functional connectivity: Statistical dependence between neurophysiological signals from distinct brain regions, often estimated via correlation or phase synchrony.

Small-world network: A graph exhibiting high clustering coefficient along with short characteristic path length, indicating both local segregation and global integration.

Clustering coefficient: A measure of the degree to which nodes in a network tend to cluster together, reflecting local connectivity density.

Characteristic path length: The average shortest path between all pairs of nodes, representing network integration efficiency.

Hub region: A network node with high centrality, pivotal for information flow and particularly vulnerable in neurodegenerative processes.

Binarisation: The conversion of weighted connectivity matrices into binary graphs based on thresholds or spanning structures to simplify network analysis.

References

1. Neurophysiological trajectories in Alzheimer’s disease progression. eLife (2024).
2. Small World derived index to distinguish Alzheimer’s type dementia and healthy subjects. Age and Ageing (2024).
3. Altered EEG Theta and Alpha Band Functional Connectivity in Mild Cognitive Impairment During Working Memory Coding. IEEE Transactions on Neural Systems and Rehabilitation Engineering (2024).
4. Activity Dependent Degeneration Explains Hub Vulnerability in Alzheimer's Disease. PLOS Computational Biology (2012).
5. Functional Brain Networks: Does the Choice of Dependency Estimator and Binarization Method Matter?. Scientific Reports (2016).