Local Geometric and Transport Properties of Networks Generated from Hyperuniform Point Patterns

Authors: James V. Raj, Xiaohan Sun, Charles Emmett Maher, Katherine A. Newhall, and Mason A. Porter

This directory contains the source code used to generate the figures for the paper "Local Geometric and Transport Properties of Networks that are Generated from Hyperuniform Point Patterns".

This code analyzes the transport efficiency and robustness of Hyperuniform-Point-Pattern-Induced (HuPPI) networks compared to Poisson-Point-Pattern-Induced (PoPPI) networks. It includes implementations for generating four types of geometric graphs (Delaunay, Gabriel, Voronoi, and Delaunay-centroidal) and calculating measurements including Total Effective Resistance (TER), Ollivier-Ricci Curvature (ORC), Random-Walk Mixing Times, and network robustness.

Figure Mapping

Directory	Manuscript Figure	Description
fig1/	Figure 1	Normalized TER (ℛ_norm) vs Disorder Strength (a)
fig2/	Figure 2	Normalized TER (ℛ_norm) vs Network Size (n)
fig3/	Figure 3	Random-Walk Mixing Time vs Disorder Strength (a)
fig4/	Figure 4	Histograms of ORC Distributions
fig5/	Figure 5	Mean ORC vs Disorder Strength (a)
fig6/	Figure 6	Mean ORC vs Network Size (n)
fig7/	Figure 7	Scatter plots: ORC (κ) vs TER Edge Contribution (Δℛ_tot)
fig8/	Figure 8	Robustness (LCC Size) under Edge Removal
supp/	Supplementary	Random-Walk Mixing Time (Bar Chart)

Setup

1. Install the required dependencies:

pip install -r requirements.txt

2. Make sure you're in the HuPPI-Network-Analysis directory before running any scripts.

Directory Structure

HuPPI-Network-Analysis/
├── utils/                   # Shared utility modules
│   ├── network/
│   │   ├── generators.py    # LatticeGenerator and GraphGenerator classes
│   │   └── measures.py      # Network_Measures class (curvature, resistance, etc.)
│   └── helpers/
│       └── common.py        # Helper utilities (UnionFind, validation, etc.)
├── fig1/                    # Figure 1: TER vs Disorder Strength
├── fig2/                    # Figure 2: TER vs Network Size
├── fig3/                    # Figure 3: Mixing Time vs Disorder Strength
├── fig4/                    # Figure 4: ORC Distribution Histograms
├── fig5/                    # Figure 5: Mean ORC vs Disorder Strength
├── fig6/                    # Figure 6: Mean ORC vs Network Size
├── fig7/                    # Figure 7: ORC vs TER Correlation
├── fig8/                    # Figure 8: Network Robustness
├── supp/                    # Supplementary: Mixing Time Bar Chart
├── requirements.txt
└── README.md

Usage

General Workflow

For each figure, the workflow is:

1. Generate Data: Run generate_data.py (or make_data.py for fig4) to create the necessary data files
2. Create Plots: Run plot.py to generate the figure from the data

Running Individual Figures

Navigate to the HuPPI-Network-Analysis directory, then run:

# Figure 1: Normalized TER vs Disorder Strength
cd fig1
python generate_data.py
python plot.py

# Figure 2: Normalized TER vs Network Size
cd fig2
python generate_data.py
python plot.py

# Figure 3: Random-Walk Mixing Time vs Disorder Strength
cd fig3
python generate_data.py
python plot.py

# Figure 4: ORC Distribution Histograms
cd fig4
python make_data.py    # Note: uses make_data.py instead of generate_data.py
python plot.py

# Figure 5: Mean ORC vs Disorder Strength
cd fig5
python generate_data.py
python plot.py

# Figure 6: Mean ORC vs Network Size
cd fig6
python generate_data.py
python plot.py

# Figure 7: ORC vs TER Edge Contribution (Scatter plots)
cd fig7
python generate_data.py
python plot.py

# Figure 8: Network Robustness (Edge Removal)
cd fig8
python generate_data.py
python plot.py

# Supplementary: Mixing Time Bar Chart
cd supp
python generate_data.py
python plot.py

Using the Master Script

You can also use the master script to run any figure:

python run_figure.py 1 both      # Generate data and plot for Figure 1
python run_figure.py 5 generate  # Only generate data for Figure 5
python run_figure.py 8 plot      # Only plot (assuming data exists) for Figure 8
python run_figure.py supp both   # Run supplementary figure

Configuration

Each figure has a config.py file (where applicable) that contains:

• Data generation parameters (lattice size, ensemble size, alpha values, etc.)
• Plotting parameters (figure size, colors, fonts, etc.)
• Output directories

You can modify these parameters to customize the experiments.

Graph Types

The code generates four types of geometric graphs from point patterns:

• Delaunay: Delaunay triangulation
• Gabriel: Gabriel graph (subset of Delaunay)
• Delaunay-centroidal: Graph connecting centroids of Delaunay simplices
• Voronoi: Voronoi tessellation graph

Point Patterns

Two types of point patterns are compared:

• Hyperuniform (Class I): Perturbed lattice points with controlled disorder
• Poisson (Random): Uniformly distributed random points

Key Metrics

• ORC (Ollivier-Ricci Curvature): Edge-level curvature measure
• TER (Total Effective Resistance): Network connectivity/transport measure
• Mixing Time: Random walk convergence measure
• LCC (Largest Connected Component): Robustness measure under edge removal

Output

Generated plots are saved to a plots/ subdirectory within each figure folder. Data files are saved to a data/ subdirectory (created automatically).