Functional Connectivity GNNs

• Functional connectivity graph neural networks are models that represent neuroimaging data as graphs, where nodes are brain regions and edges capture statistical dependencies.
• They employ both static and dynamic graph constructions, integrating techniques like sliding windows and transformer-based embeddings to enhance temporal and multimodal analyses.
• These methods have achieved state-of-the-art results in disease classification and cognitive decoding, proving valuable for biomarker discovery and advanced brain connectivity research.

Functional connectivity graph neural networks are graph neural network (GNN) methods in which neuroimaging or electrophysiological data are represented as graphs whose nodes correspond to brain regions of interest or EEG channels and whose edges encode statistical dependency between signals, most commonly functional connectivity derived from BOLD or EEG time series. Within network neuroscience, these models support graph-level classification, state decoding, causal or effective connectivity estimation, biomarker discovery, dynamic connectome modeling, and multimodal fusion with structural connectivity; in later work, the same brain-inspired principle is generalized beyond neuroscience by pairing structural message passing with a functional connectivity block based on persistent graph homology (Bessadok et al., 2021, Li et al., 7 Aug 2025).

1. Conceptual basis and scope

In the network neuroscience formulation reviewed in "Graph Neural Networks in Network Neuroscience" (Bessadok et al., 2021), a brain graph is formalized as $G=(N,E,\mathbf{A},\mathbf{F})$, where $\mathbf{A}\in\mathbb{R}^{n\times n}$ is the adjacency matrix and $\mathbf{F}\in\mathbb{R}^{n\times f}$ is the node feature matrix. For functional brain graphs, nodes represent ROIs and edges represent statistical dependencies, often Pearson correlation, between regional BOLD time series; one common construction is

$$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$

The same formalism has been used for rs-fMRI, task fMRI, and EEG, although the node semantics differ by modality (Bessadok et al., 2021, Kim et al., 2020, Zhdanov et al., 2022).

A central distinction in this literature is between structural, functional, and effective connectivity. Structural connectivity encodes physical white-matter tracts, typically from DTI or DSI; functional connectivity encodes statistical codependency or correlation; effective or causal connectivity attempts to model directed influence or information flow (Wein et al., 2020, Yu et al., 2022). This distinction matters because many GNN pipelines begin from undirected correlation graphs, whereas other methods explicitly learn directed acyclic graphs or perturbation-based directed influence measures.

Another recurring distinction is between local structural propagation and global functional dependence. Conventional GNNs aggregate along an input adjacency, but several works argue that this can miss higher-order, delayed, dynamic, or cross-modal interactions. The literature therefore includes methods that learn task-aware graphs from time series, model positive and negative connectivity separately, operate on edge-to-edge relationships, incorporate temporal evolution, or couple structural and functional modalities (Yu et al., 2022, Karmi et al., 30 Mar 2026, Yang et al., 21 Apr 2025, Zhao et al., 2023, Yin et al., 2024, Li et al., 7 Aug 2025).

2. Graph construction from functional data

Functional connectivity graph construction varies substantially across modalities and tasks. In rs-fMRI and task fMRI, the standard pipeline is parcellation, extraction of regional time series, and computation of pairwise correlation. In the GIN study on rs-fMRI, each subject is represented by a graph with 400 ROIs from the Schaefer400 parcellation, edges given by thresholded top-$M$-percentile Pearson correlation values, and one-hot node features encoding ROI identity (Kim et al., 2020). In the EEG framework for schizophrenia and auditory verbal hallucinations, each sample is represented as $G=(\mathbf{A},\mathbf{X})$ with $\mathbf{X}\in\mathbb{R}^{61\times 100}$ and $\mathbf{A}\in\mathbb{R}^{61\times 61}$, where the 61 nodes correspond to EEG channels (Zhdanov et al., 2022).

Dynamic formulations replace a single static adjacency with a time-indexed sequence of graphs. GraphCorr partitions BOLD signals into partially overlapping windows, computes window-specific dynamic FC

$$\mathbf{FC}_{i,j,w}=\mathrm{Corr}(\mathbf{F}_{i,\cdot,w},\mathbf{F}_{j,\cdot,w}),$$

and additionally computes lagged cross-correlations across a range of time lags (Sivgin et al., 2023). SMC-GCN likewise uses a sliding-window approach and constructs a graph $\boldsymbol{O}_t=\{A_t,F_t\}$ at each time window from fMRI, with nodes as ROIs and edges typically computed via partial correlation (Zhao et al., 2023). ST-MAE treats the input as a dynamic graph sequence $\mathbf{A}\in\mathbb{R}^{n\times n}$0 and reconstructs masked node features and masked adjacencies over time (Choi et al., 2023).

Several papers depart from standard node-to-node FC. The edge-boosted framework argues that node-based connectivity does not accurately capture “functional connections” and introduces edge functional connectivity (eFC), where an edge time series is formed by the elementwise product

$\mathbf{A}\in\mathbb{R}^{n\times n}$1

of z-scored ROI time series, followed by an $\mathbf{A}\in\mathbb{R}^{n\times n}$2 eFC matrix capturing similarity between edges themselves (Yang et al., 21 Apr 2025). The signed visual-category decoder constructs parcel-level functional graphs from 7T fMRI, computes Pearson correlations, and decomposes them into positive and negative channels,

$\mathbf{A}\in\mathbb{R}^{n\times n}$3

yielding a two-channel signed connectivity graph (Karmi et al., 30 Mar 2026).

Multimodal formulations add structural information. The DCRNN framework uses DTI-derived weighted adjacency $\mathbf{A}\in\mathbb{R}^{n\times n}$4 as the anatomical backbone and fMRI BOLD signals as temporally evolving node signals (Wein et al., 2020). The heterogeneous GNN for MCI diagnosis builds a subject-level heterogeneous graph with functional adjacency $\mathbf{A}\in\mathbb{R}^{n\times n}$5, structural adjacency $\mathbf{A}\in\mathbb{R}^{n\times n}$6, and cross-modal hetero-meta-paths collected into

$\mathbf{A}\in\mathbb{R}^{n\times n}$7

where $\mathbf{A}\in\mathbb{R}^{n\times n}$8 combines node-level structure-function coupling and community-level cross-modal relations (Yin et al., 2024).

Representation	Construction	Example
Static ROI graph	Pearson-correlation adjacency over ROI time series	(Kim et al., 2020)
EEG channel graph	$\mathbf{A}\in\mathbb{R}^{n\times n}$9 adjacency with $\mathbf{F}\in\mathbb{R}^{n\times f}$0 node features	(Zhdanov et al., 2022)
Dynamic FC sequence	Sliding-window graphs and lag-aware features	(Sivgin et al., 2023)
Edge functional graph	Edge time series and $\mathbf{F}\in\mathbb{R}^{n\times f}$1 eFC matrix	(Yang et al., 21 Apr 2025)
Signed FC graph	Separate positive and negative adjacency channels	(Karmi et al., 30 Mar 2026)
Multimodal heterogeneous graph	FC, SC, and hetero-meta-path fusion	(Yin et al., 2024)

3. Architectural families

The simplest FC-GNN pipelines combine a graph encoder with graph-level pooling and a classifier. In the EEG framework, an encoder of three 1D convolutional layers maps raw per-channel signals to a $\mathbf{F}\in\mathbb{R}^{n\times f}$2 embedding, a GraphConv layer maps this to $\mathbf{F}\in\mathbb{R}^{n\times f}$3, and a classifier applies GlobalMaxPooling and linear layers to produce three outputs corresponding to schizophrenia with hallucinations, schizophrenia without hallucinations, and healthy controls (Zhdanov et al., 2022). The rs-fMRI GIN study uses a 5-layer GIN with 64 hidden units per layer, one-hot node features, sum-pooled graph features, and Infomax regularization for binary sex classification (Kim et al., 2020).

A second family emphasizes temporal dynamics. The DCRNN framework adopts a sequence-to-sequence encoder-decoder architecture built from diffusion-convolutional gated recurrent units, with spatial propagation defined over powers of the transition matrix $\mathbf{F}\in\mathbb{R}^{n\times f}$4: $\mathbf{F}\in\mathbb{R}^{n\times f}$5 This explicitly couples spatial diffusion and recurrent temporal modeling (Wein et al., 2020). GraphCorr uses a transformer-based node embedder over windowed FC matrices, a lag filter over delayed cross-correlations, and message passing that fuses node embeddings with lag features before handing enhanced features to downstream models (Sivgin et al., 2023). SMC-GCN goes further by treating particles as entire latent graphs $\mathbf{F}\in\mathbb{R}^{n\times f}$6 and using a GCN as the nonlinear state transition in a sequential Monte Carlo framework (Zhao et al., 2023).

A third family replaces fixed FC with learned or task-aware connectivity. TBDS learns a directed acyclic graph from multivariate fMRI time series using an SVAR-style formulation,

$\mathbf{F}\in\mathbb{R}^{n\times f}$7

with acyclicity enforced by

$\mathbf{F}\in\mathbb{R}^{n\times f}$8

The resulting graph is then processed by a modified GCN that separates positive and negative edges (Yu et al., 2022). BrainGNN learns a subject-specific directed weighted graph via self-attention over region embeddings and applies GRU-based message passing with repeated top-$\mathbf{F}\in\mathbb{R}^{n\times f}$9 pooling for region selection (Mahmood et al., 2021).

A fourth family emphasizes topology, signed structure, or graph transformers. CycGAT constructs a cycle incidence matrix, a cycle adjacency matrix, and topology-aware attention with edge positional encodings in cycles, thereby operating on edges in a cycle domain rather than only on nodes in the original graph (Huang et al., 2024). The signed category decoder uses two signed graph convolution layers, a learnable sparse symmetric mask $$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$0, and class-specific gradient–input saliency (Karmi et al., 30 Mar 2026). GGT combines node features, position encodings from random walks and MNI coordinates, and a learned gate $$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$1 that modulates attention-weighted message passing (Qu et al., 2024).

A fifth family is explicitly multimodal. The heterogeneous GNN for MCI diagnosis uses Heterogeneous Graph Attention Network layers over homo-meta-paths and hetero-meta-paths, then applies a heterogeneous graph pooling strategy that separately pools different node types to avoid feature confusion (Yin et al., 2024). The later FC-GNN framework generalizes this multimodal intuition to arbitrary graphs: a structural GNN processes the original graph, while a functional connectivity block computes pairwise functional dependencies from node features, extracts persistent graph homology, embeds birth and death sets by inverse transform sampling, and fuses functional and structural embeddings by concatenation or elementwise addition (Li et al., 7 Aug 2025).

4. Interpretability, saliency, and biological localization

Interpretability is a persistent concern because many connectome models must support neuroscientific inspection rather than prediction alone. One strategy is subgraph explanation. The EEG schizophrenia study uses GNNExplainer, which searches for the smallest subgraph and minimal set of node features most influential for a prediction by masking the adjacency and feature matrices, thereby identifying characteristic task-depending connectivity and validating the resulting patterns against current domain knowledge (Zhdanov et al., 2022).

A second strategy transfers saliency methods from CNNs into graph space. The rs-fMRI GIN paper argues that GIN is a dual representation of a CNN in graph space, with the adjacency matrix acting as a generalized shift operator. This motivates an input-layer saliency score

$$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$2

which is particularly interpretable when node features are one-hot ROI identities (Kim et al., 2020). That work reports that the obtained saliency map shows high correspondence with previous neuroimaging evidences related to sex differences.

A third strategy is explicit sparsification or selection. BrainGNN applies repeated top-$$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$3 pooling to retain the most relevant brain regions for schizophrenia classification, while TBDS encourages sparse task-aware DAGs through $$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$4 penalties and the DAG constraint (Mahmood et al., 2021, Yu et al., 2022). The signed visual-category decoder learns a sparse near-binary edge mask shared across categories and complements it with class-specific saliency maps,

$$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$5

which reveal reproducible subnetworks for food, sports, and vehicle decoding (Karmi et al., 30 Mar 2026).

Attention weights are also used as explanatory objects. GGT interprets average attention heatmaps as significant neural connectivities for WRAT prediction, highlighting connections within and between Auditory, Visual, Memory Retrieval, Default Mode, Sensory/Somatomotor, and Subcortical networks (Qu et al., 2024). CycGAT interprets its sparsified edge-domain output as a functional backbone with significantly fewer cycles than raw FC, concentrating retained connections in occipital, prefrontal, and cerebellar regions (Huang et al., 2024). This suggests that interpretability in FC-GNNs is increasingly tied not only to node saliency, but also to topology-aware notions such as signed relevance, cycle reduction, and structure-function coupling.

5. Applications and reported performance

Disease classification remains the dominant application. In schizophrenia, the EEG graph framework reports state-of-the-art performance for differentiating schizophrenia patients with and without auditory verbal hallucinations and healthy controls, while also distinguishing listening state from resting state (Zhdanov et al., 2022). BrainGNN reports state-of-the-art classification performance on a schizophrenia fMRI dataset and disorder-relevant sparse region selection (Mahmood et al., 2021). In autism, SMC-GCN on ABIDE reports 73.64 $$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$6 accuracy and 75.29 $$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$7 AUC, exceeding SVM, RF, GCN, GAT, and BrainGNN in the reported 5-fold cross-validation table (Zhao et al., 2023).

Task-aware or multimodal graph learning has also been evaluated at scale. TBDS reports PNC AUROC 83.4 and accuracy 76.9, and ABCD AUROC 94.2 and accuracy 88.0, outperforming reported fixed-graph and learnable-graph alternatives; the paper notes that GNN-DAG is too slow on large ABCD (Yu et al., 2022). The heterogeneous dual-modal HGNN for ADNI-3 reports a mean classification accuracy of 93.3% for MCI diagnosis and an AUC of 0.961 for NC vs. MCI (Yin et al., 2024). The edge-boosted graph learning model reports 0.800 $$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$8 0.088 accuracy on ADNI and 0.708 $$\mathbf{A}_{ij}=\mathrm{corr}(\text{BOLD}_i,\text{BOLD}_j).$$9 0.057 on PPMI, outperforming CNN, GCN, CRGNN, and MGNN in the reported table (Yang et al., 21 Apr 2025).

Several works target cognitive or perceptual decoding rather than disease. The GIN rs-fMRI study reports that GIN+Infomax achieved 84.6% accuracy, outperforming baseline GCN at 83.9%, for sex classification on approximately 950 HCP subjects (Kim et al., 2020). GraphCorr, used as a plug-in feature extractor, reports substantial gains in accuracy and ROC-AUC across SAGE, GCN, BrainGNN, and BrainNetCNN; on HCP/Schaefer, the reported gains include +14.4%/+9% for SAGE and +10.8%/+8.5% for GCN (Sivgin et al., 2023). GGT reports RMSE 14.55 $M$0 0.75 on emoid and 14.80 $M$1 0.53 on nback, outperforming LR, GCN, MTL, M2TL, and NM2TL for WRAT prediction (Qu et al., 2024). The signed visual-category decoder reports right-hemisphere accuracy 0.78 $M$2 0.06 and Macro-AP 0.88 $M$3 0.06, with per-class AP 0.92 for food, 0.88 for sports, and 0.84 for vehicle (Karmi et al., 30 Mar 2026).

Beyond neuroscience, the 2025 FC-GNN framework explicitly generalizes functional-connectivity reasoning to graph-level classification across diverse networks. On 13 datasets, the dual-modality FC-GNNs are reported to achieve mean gains of +5.33% accuracy and -1.68% variance over single-modality baselines; specific examples include ENZYMES improving from 36.50% with GIN to 46.94% with FC-MLP-GIN, and COLLAB improving from 57.97% to 76.30% with FC-MLP-GCN (Li et al., 7 Aug 2025). A plausible implication is that the term “functional connectivity GNN” now denotes both a neuroimaging methodology and a transferable graph-learning design pattern.

Setting	Reported result	Paper
ABIDE ASD vs. HC	Accuracy 73.64 $M$4, AUC 75.29 $M$5	(Zhao et al., 2023)
PNC task-aware DAG	AUROC 83.4, Accuracy 76.9	(Yu et al., 2022)
ABCD task-aware DAG	AUROC 94.2, Accuracy 88.0	(Yu et al., 2022)
ADNI-3 MCI diagnosis	Mean accuracy 93.3%, AUC 0.961	(Yin et al., 2024)
7T visual category decoding	Accuracy 0.78 $M$6 0.06, Macro-AP 0.88 $M$7 0.06	(Karmi et al., 30 Mar 2026)
General graph classification	Mean gains +5.33% accuracy, -1.68% variance	(Li et al., 7 Aug 2025)

6. Limitations, misconceptions, and active directions

A common misconception is that functional connectivity graphs are synonymous with causal brain graphs. The literature does not support that equivalence. Standard FC graphs are usually undirected similarity graphs; directed influence is introduced only in specialized formulations such as perturbation-based DCRNN influence measures or task-aware DAG learning (Wein et al., 2020, Yu et al., 2022). Another misconception is that a single static correlation matrix is sufficient for all tasks. Multiple papers explicitly argue that temporally static FC reduces sensitivity to dynamic features of brain activity, or that stationary and noise-free graph assumptions are too restrictive (Sivgin et al., 2023, Zhao et al., 2023, Choi et al., 2023).

Methodological trade-offs are equally explicit. The DCRNN paper notes that the anatomical backbone constrains all modeled interactions and that its quality and limitations influence inferred connectivity; BOLD signal temporal limits remain (Wein et al., 2020). The edge-boosted framework highlights the high dimensionality of eFC matrices, which scale quadratically with the number of edges, and notes an interpretability trade-off relative to standard ROI-based analysis (Yang et al., 21 Apr 2025). ST-MAE argues that contrastive graph perturbations can destroy crucial semantic information in brain graphs and proposes generative masked reconstruction instead (Choi et al., 2023).

Sample scarcity and cross-dataset generalization are another major theme. DCRNN reports that pretraining on HCP and fine-tuning on an independent small dataset acquired with a different scanner and protocol achieves approximately 27% lower testing error than random-initialized training (Wein et al., 2020). ST-MAE reports large-scale pretraining on more than 50,000 fMRI datasets and improved robustness in low-label settings (Choi et al., 2023). The heterogeneous HGNN introduces graph data augmentation for imbalance, while GraphCorr is designed as a plug-in module that can raise temporal sensitivity in multiple downstream models (Yin et al., 2024, Sivgin et al., 2023).

Current directions point toward richer graph semantics rather than a single canonical FC construction. These directions include signed positive/negative interactions, cycle-based topology, edge-centric connectivity, dynamic latent-state inference, heterogeneity across modalities, and persistent-homology summaries of functional organization (Karmi et al., 30 Mar 2026, Huang et al., 2024, Yang et al., 21 Apr 2025, Zhao et al., 2023, Yin et al., 2024, Li et al., 7 Aug 2025). This suggests that functional connectivity graph neural networks are better understood as a family of graph learning strategies centered on statistical interdependence, temporal variation, and multimodal complementarity, rather than as one fixed architecture or one fixed definition of brain connectivity.