Participation in Percolation (PiP): A Data-Driven Measure of Network Hubs in Functional Brain Networks

Brady J. Williamson¹, Minarose Ismail^2,3, Darren S Kadis^2,3

¹University of Cincinnati College of Medicine, Department of Radiology, Cincinnati, OH, USA
²Neurosciences and Mental Health, Hospital for Sick Children, Toronto, ON, Canada
³Department of Physiology, University of Toronto, Toronto, ON, Canada

Overview

PiP (Participation in Percolation) is a toolbox for identifying network hubs using a data-driven approach based on probabilistically sampled node attacks and percolation-based collapse analysis.

To validate the method and demonstrate its biological relevance, we apply PiP to magnetoencephalography (MEG) data collected during an expressive language task in a pediatric cohort, localizing functionally relevant language network hubs.

This repository accompanies the study:

"Participation in Percolation: A Data-Driven Measure of Network Hubs in Functional Brain Networks"
Williamson et al., 202x

Analysis Pipeline

To run the full pipeline on included data:

1. Run the attack simulation
   scripts/1_PiP_attack.m
   → Input: binary adjacency matrices (data/adjacency_matrices/)
   → Output: node participation matrices (results/)

2. Visualize node participation surfaces
   scripts/2_viz_attack_surf.ipynb
   → Input: node participation matrices in results/
   → Output: subject-level PiP surface plots

   Example Output for 1 subject:
   

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3. Perform consensus clustering to identify critical hubs
   3_consensus_clustering.ipynb
   → Input: node participation matrices in results/
   → Output: critical node consensus map and group-level results (figures/PiP_group_consensus/)

   Example Output:
   

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4. Compute graph-theory hub metrics
   4_compute_hub_metrics.m
   → Input: Binary adjacency matrices (data/adjacency_matrices/) → Output: Degree, betweenness, and PageRank metrics (results/graph_hub_metrics/)

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5. Compare PiP results with classical hub metrics
   5_compare_metrics_consensus.py
   → Input: PiP and graph-theory hub matrices
   → Output: Jaccard comparisons + consensus clustering figures(figures/PiP_group_consensus/)

   PiP map:
   Degree map:
   Betweenness map:
   PageRank map:
   

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