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Graph analysis of functional brain networks: practical issues in translational neuroscience
Fabrizio De Vico Fallani, Jonas Richiardi, Mario Chavez, Sophie Achard
TL;DR
Graph analysis offers a systems-level way to study brain dysfunction, but its translational use is complicated by methodological choices throughout the analysis pipeline. This review synthesizes practical guidance on constructing and interpreting functional brain graphs, highlighting clinical applications alongside limitations in filtering, variability, and measurement effects. It concludes that careful, physiologically relevant analysis is needed to avoid counterproductive application.
Problem
Graph analysis is increasingly used to characterize multifaceted brain disorders, yet rapid methodological development and limited validation leave practical reliability and physiological relevance insufficiently resolved.
Method
The review provides focused practical indications for functional brain-network analysis, covering methodological steps, graph metrics, statistical procedures, and common pitfalls.
Results
Graph analysis has revealed altered small-world organization and efficiency across disorders and population groups, while providing clinical and cognitive insights at multiple topological scales.
Takeaways & Limitations
Functional brain-graph findings should be interpreted through the complete processing pipeline and the physiological relevance of the neural phenomenon under study.
Takeaways & Limitations
Graph filtering lacks an objective threshold-selection criterion, and statistical variability from noisy activity to topological metrics remains without a complete evaluation framework.
Abstract
from arXiv · showhide
The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.
1. INTRODUCTION
Functional brain networks represent temporal dependence among regional activities as graph structure, enabling topological analysis of organization and dysfunction. The review argues that meaningful use requires methodological expertise across the processing pipeline and physiological knowledge of the phenomenon studied.
- Functional brain networks: Functional connectivity measures temporal dependence between regional brain activities and produces an N × N representation that can be treated as a graph.The framework applies to fMRI, EEG, and MEG signals.
- Graph analysis: Graph metrics characterize small-world organization, identify central areas, and detect communities of densely interconnected regions.Examples include clustering coefficient, path length, efficiency, degree, betweenness, closeness, and eigenvector centrality.
- Open issues: Brain graph analysis has progressed rapidly, but single metrics may have low clinical sensitivity and specificity, while link-wise comparisons can ignore network topology.The authors describe understanding of brain organization at the network level as still in its infancy.
- Open issues: Functional network construction requires signal-quality improvement, connectivity estimation, link filtering, graph-metric extraction, and statistical analysis.The review presents this as a tricky processing pipeline requiring practical reliability and physiological relevance.
2. BRAIN... NETWORKS OR GRAPHS?
The paper distinguishes structural networks, whose links represent axonal pathways, from functional graphs, whose links are statistical temporal dependencies. It recommends “graphs” for functional connectivity because the term emphasizes mathematical modeling without assumptions about link nature.
- Terminology: The term “network” spans connected systems with different meanings across disciplines, creating potential misunderstanding.Neuroscience may use it for regions simultaneously active during a mental state or for connectivity-based representations.
- Terminology: Structural brain networks have links representing estimated axonal fiber tracks, whereas functional connectivity links represent statistical temporal dependence.The distinction concerns what the links are understood to represent.
- Terminology: For functional connectivity, “graphs” is more cautious than “networks” because it avoids explicit assumptions about the nature of links.The authors present this terminology as a way to improve interdisciplinary exchange.
3. BRAIN NODES
Brain-node definition depends on recording modality and spatial scale. Choices include voxels, anatomical or data-driven aggregates, ICA components, sensors, or reconstructed cortical sources, each with practical trade-offs and biases.
- Modality-specific nodes: Voxel-based modalities define nodes in measurement space, while sensor-based modalities assign nodes to sensors or reconstructed sources.This distinction applies broadly to fMRI, PET, EEG, MEG, and fNIRS.
- Voxel-based nodes: Voxel aggregation requires choosing spatial scale and a parcellation strategy, such as anatomical, data-driven, or hybrid methods.Fixed anatomical atlases are currently the most common regional approach.
- Voxel-based nodes: Single-voxel nodes provide higher resolution and model-free analysis but can reduce signal-to-noise ratio and increase graph size.Regional approaches trade some resolution for smaller graphs and potentially different comparability properties.
- Data-driven nodes: ICA maps each independent component to a node and computes connectivity from component time courses without requiring a predetermined atlas.Component stability can be assessed across runs, including with ICASSO clustering.
- Sensor-based nodes: Volume conduction makes EEG and MEG sensor signals mixtures of blurred cortical activity, potentially producing biased non-neural dependence.Possible responses include spatial filters, measures such as imaginary coherence or phase lag index, and cortical source reconstruction.
4. FUNCTIONAL LINKS
Functional-link construction is a crucial, assumption-dependent modeling step: researchers must match connectivity measures to signal properties, neurophysiological hypotheses, and the intended interpretation. The review emphasizes that different methods can yield non-equivalent results and that preprocessing, data length, stationarity, and volume-conduction effects matter.
- Link modeling: Functional connectivity links are data-driven similarities between brain signals, whereas effective-connectivity models require realistic hypotheses about putative connectivity schemes.Model-based approaches generally involve relatively few nodes and simple connectivity patterns.
- Method selection: Functional-connectivity methods differ in whether they estimate symmetric mutual interaction or asymmetric information propagation, and whether relationships are linear or nonlinear.The resulting links may be undirected or directed and weighted.
- Interpretation: Correlation sign cannot directly identify inhibitory or excitatory interactions, and Granger causality need not imply phase coherence.The authors recommend referring to the exact theoretical principle implemented by each method.
- Method selection: The appropriate connectivity method depends on dataset and method characteristics, with comparison studies reporting non-unequivocal performance.Using several methods and seeking consistency is suggested as one possible approach.
- Signal dependence: Time-domain methods suit fMRI’s low-frequency signals, while nonlinear methods require more data points for rapid changes and multivariate methods also require larger samples.Wavelet filters can isolate self-similar functional-connectivity properties in fMRI.
- Microscopic recordings: In neuronal ensembles, binary spike timing supports spike-synchrony measures that function as time-scale-dependent statistical tests of neuronal codes.These methods extend functional-connectivity analysis to microscopic electrophysiological recordings.
- Statistical assumptions: Functional-connectivity estimates become more reliable with more time points, but their bias depends on recording length and interaction effects.The statistical definitions of these measures impose assumptions on noisy signals.
- Signal dependence: Most functional-connectivity methods assume stationarity or quasi-stationarity, which may fail in task-based or diseased resting-state recordings.Head motion is a major source of non-stationarity affecting brain-graph topology; global-signal regression remains controversial.
5. GRAPH FILTERING
Graph filtering determines which functional connections are retained for topological analysis, but threshold choice requires both statistical and topological justification. Statistical thresholds test connectivity against a null hypothesis, whereas topological strategies control link density to improve comparability.
- Functional connectivity produces an N × N weighted matrix of pairwise links, while directed methods yield N(N −1) links excluding self-connectivity.
- Filtering retains the strongest connected brain-node pairs, so thresholding changes which network topology is compared.
- Statistical thresholds retain FC values whose percentile is significant relative to a theoretically derived or surrogate-generated null distribution.
- Topological thresholding controls the number of links because link density influences most graph metrics, including shortest path length.
6. TOPOLOGICAL METRICS
Topological metrics describe brain graphs at whole-brain, subgroup, or node scales, but their interpretation depends on metric definitions, graph weights, thresholds, and the research question. Weighted graphs introduce conceptual ambiguity because FC weights represent signal similarity rather than physical distance.
- 6. TOPOLOGICAL METRICS: Metrics operate at large, intermediate, or small scales, respectively describing whole graphs, subgraphs, or individual brain nodes.
- 6. TOPOLOGICAL METRICS: Metric selection requires attention because definitions can introduce mechanistic biases, including degree-correlation effects in clustering and subnetwork-size effects in hub identification.
- 6. TOPOLOGICAL METRICS: Clinical graph analysis has linked altered small-world organization to schizophrenia, autism, stroke, spinal cord injuries, and Alzheimer’s disease.
- 6. TOPOLOGICAL METRICS: Metric scale should match the research question: whole-brain indices do not describe subgroups, nodes, or links, while finer-grained analyses provide more localized information.
- 6. TOPOLOGICAL METRICS: Weighted graph distances are conceptually ambiguous because FC weights represent signal similarity; reciprocal or weight-to-distance transformations are possible remedies.
7. STATISTICAL ANALYSIS
Statistical comparison of brain graphs requires appropriate reference models, matched graph structure, and methods suited to metric distributions. The review describes hypothesis testing, statistical modeling, and classification as complementary approaches for comparing groups and relating topology to behavior.
- 7. STATISTICAL ANALYSIS: Brain graphs are compared with simulated null models or across experimental conditions and populations.
- 7. STATISTICAL ANALYSIS: Null-model choice can substantially change estimated small-world properties, especially when FC methods inflate clustering or generate spurious links.
- 7. STATISTICAL ANALYSIS: MEG and fMRI studies have related graph metrics to cognitive load, aging, and schizophrenia, including lower local efficiency with cognitive load and increased path length in schizophrenia.
- 7. STATISTICAL ANALYSIS: Comparisons require matched node number and ordering, while link count and total strength can alter graph metrics without changing underlying topology.
- 7. STATISTICAL ANALYSIS: The main statistical approaches are hypothesis testing for group differences, modeling for behavioral relations, and classification for separating graph populations.
- 7. STATISTICAL ANALYSIS: Because graph metrics may be correlated and non-Gaussian, analyses can use normalization, non-parametric tests, generalized linear models, or machine learning with cross-validation.
8. HEALTHY AND PATHOLOGICAL BRAINS
Clinical graph analysis is vulnerable to structural, vascular, motion, stress, and physiological confounds that affect node definition, correspondence, signal estimation, or connectivity measures. The review therefore emphasizes modality- and pathology-specific preprocessing and normalization choices.
- 8. HEALTHY AND PATHOLOGICAL BRAINS: Clinical patients’ structural, functional, and behavioral alterations can confound graph analysis, with effects varying by neuroimaging modality.
- 8. HEALTHY AND PATHOLOGICAL BRAINS: Lesions can disrupt segmentation, normalization, node definition, and inter-subject correspondence because their size, location, and shape vary unpredictably.
- 8. HEALTHY AND PATHOLOGICAL BRAINS: Gray-matter atrophy or partial-volume effects can reduce assigned voxels and create an apparent decrease in functional connectivity for affected nodes.
- 8. HEALTHY AND PATHOLOGICAL BRAINS: Vascular pathology can disrupt BOLD-based FC by altering regional vessel dilation, motivating deconvolution with flexible hemodynamic models.
- 8. HEALTHY AND PATHOLOGICAL BRAINS: Group differences in motion, stress, cardiac activity, or respiration can confound fMRI and EEG analyses, although preprocessing and data-driven alternatives are available.
9. ABSTRACTION LEVELS
Graph analysis operates at a higher abstraction level than brain activity and functional connectivity, so graph results should be interpreted through the connectivity measure and imaging technique rather than attributed directly to neural processes.
- Graph analysis depends on functional connectivity, which depends on measured brain activity, linking multivariate, bivariate, and univariate methods.
- Interpreting graph results requires accounting for the selected functional-connectivity measure and neuroimaging technique.
- Increasing abstraction provides complementary information but makes graph results less intuitively interpretable in relation to the original neural process.
- Graph-metric changes can be associated with functional-connectivity changes but not directly with changes in measured brain signals.
10. FUTURE CHALLENGES
Future challenges concern the methodological reliability, dynamical representation, and multiscale integration of functional brain graphs. These challenges include threshold selection, uncertainty propagation, dynamic networks, and coherent modeling across space and time.
- No objective criterion for selecting the connectivity threshold T forces repeated analyses across increasing thresholds, becoming time-consuming as graphs, subjects, or conditions grow.
- Topological metrics lack a predefined variability assessment because they derive from connectivity patterns with unknown probability distributions.
- Functional brain networks change across both long timescales, such as plasticity after lesions, and short timescales, such as cognitive or motor learning.
- Tracking individual topological metrics over time addresses dynamic networks but remains an oversimplified methodological approach.
- A comprehensive theory is still lacking for dynamic brain graphs combining multiple node and link features across spatial and temporal scales.
11. THE ROLE OF TECHNOLOGY
Technology can broaden access to graph analysis and help integrate findings, but clinical adoption and consensus remain constrained by methodological complexity and many analysis choices.
- Graph analysis requires methodological expertise, limiting its clinical impact where simple and fast tools are needed for routine adoption.
- Many tunable methods and parameters increase analytical degrees of freedom and disperse findings, complicating consensus about disease-related network properties.
- International brain initiatives can accelerate progress by combining knowledge from neuroimaging centers and providing access to data, platforms, and infrastructures.
12. CONCLUSIONS
Graph analysis offers a systems-level approach to multifaceted neurological disease, but its growing clinical popularity also creates a risk of rushed and counterproductive application. The review therefore provides practical guidance for interpreting functional brain-network analyses and avoiding common traps.
- Neurological cognitive and motor impairments have been hypothesized to involve dysfunction across many interacting remote regions rather than a single area.
- Systems-level tools create opportunities for more complete understanding of brain diseases and for network-based neuromarkers supporting early diagnosis and prognosis.
- The review addresses the risk of frenetic graph-theoretical application by offering focused indications for making sense of functional brain-network analysis and avoiding common traps.