Structure–Function Coupling/Decoupling (Graph-Spectral Framework)

This repository contains code used in:

Xing Qian et al. (2026)
Altered salience network structure–function integration underlies the decline in cognitive flexibility during aging
PLOS Biology

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Overview

This implementation is based on:

Medaglia et al. (2018), Nature Human Behaviour

Key difference

Instead of selecting a fixed number of eigenmodes, we use a variance-based criterion to determine:

• Coupling (alignment; smooth components)
• Decoupling (liberality; rough components)

This approach:

• Is data-driven
• Is robust across parcellations
• Avoids arbitrary selection of k

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Methods

1. Component selection (choose_k.m)

Steps:

1. Divide eigenvalues into:

   • Smooth (positive eigenvalues)
   • Rough (negative eigenvalues)

2. For each group:

   • Compute total energy = sum of absolute eigenvalues
   • Sort eigenvalues (descending)
   • Compute cumulative energy

3. Define kA and kL as:

   • Minimum number of eigenvalues explaining 95% energy

4. Average across time → KA, KL

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2. Signal decomposition (signal_decomposition.m)

Structural matrix:

A = V Λ V^T

• V: eigenvectors
• Λ: eigenvalues

Interpretation:

• Smooth modes → coherent activity
• Rough modes → abrupt variation

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Graph Fourier Transform

x_hat = V^T x

Reconstruction:

x = V x_hat

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Coupling / Decoupling

• Coupling = projection onto smooth modes
• Decoupling = projection onto rough modes

Use KA and KL to select components.

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Notes

• This is NOT SC–FC correlation
• It is graph spectral decomposition

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Citation

Please cite:

• Qian et al., 2026 (PLOS Biology) DOI 10.5281/zenodo.19316674
• Medaglia et al., 2018