Proximity Graphs

This directory contains comprehensive documentation for the Proximity Graphs Python library.

Library Overview

The Proximity Graphs library provides tools for:

• Generating and manipulating point sets in n-dimensional space

• Creating various types of geometric and proximity graphs

• Analyzing graph properties (degrees, lengths, orientations, entropy)

• Visualizing graphs and point patterns

Main Components

Contents:

• Usage
  • Installation
• Quick Reference Guide
  • Creating Points
  • Transforming Points
  • Creating Graphs
  • Graph Operations
  • Visualization
  • Analysis
  • Data Export
  • Common Patterns
  • Tips and Tricks
  • Performance Considerations
  • Troubleshooting
  • Further Reading
• Points
  • SetPoints
  • Constructor
  • Submodules
• Usage Tips
• Common Workflows
  • Generate and Transform Points
  • Create Custom Point Patterns
• GeometricGraphs
  • Overview
  • Class: GeometricGraph
  • Constructors
  • Submodules
• ProximityGraph
  • Overview
  • Base Class: ProximityGraph
  • Submodules
• Biological Graphs
  • Introduction
  • Concept and Motivation
  • Available Implementations
  • Usage Patterns
  • References
  • Contributing
• Experiments
  • Introduction
  • Key Features
  • Quick Installation
  • Basic Usage
  • Detailed API
  • Main Methods
  • Advanced Configuration
  • Complete Examples
  • Typical Workflow
  • Tips and Best Practices
  • Troubleshooting
  • Quick Reference
• Example notebooks
  • draw2 method
  • Customization
  • Gamma Graph
  • Single Neighborhood, 512*24=12288 points
  • Two Neighborhoods
  • Special cases, 100 points
  • Examples 100 points
  • Special cases, 1000 points
  • Examples 1000 points
  • Test Alpha Shapes Y Alpha Hulls
  • Plotting with method draw_grid
  • No method
  • draw method
  • \(\gamma\)-graph
  • Delaunay Triangulation
  • Convex Hull
  • \(\alpha\)-shape
  • \(\alpha\)-hull
  • \(\beta\)-skeleton con \(\beta \in [0, \infty)\)
  • Gabriel Graph
  • Relative Neighborhood Graph
  • MST
  • Stepping Stone
  • NNG
  • Sigma Graph
  • Unit Disk
  • SIG
  • Eliptic GG
  • Custom kwargs
  • Test Gamma Graph
  • Test Set Points
  • EXAMPLE 1: Basic Experiment - Comparing Gabriel vs RNG
  • EXAMPLE 2: Multiple Graph Types with Different Point Distributions
  • EXAMPLE 3: Custom Metrics
  • EXAMPLE 4: Biological Graphs - Physarum
  • EXAMPLE 5: Parameter Sweep
  • EXAMPLE 6: Different Point Distributions
  • EXAMPLE 7: Storing and Retrieving Graphs
  • EXAMPLE 8: Advanced - Entropy Analysis
  • EXAMPLE 9: Point Transformations
  • Testbio
  • Times
• References
  • Classical proximity graphs and computational geometry
  • Specialized proximity graph families
  • Machine learning, clustering, and manifold learning
  • Biological and adaptive networks
  • Spatial networks, roads, and movement corridors
  • Software and scientific computing
  • General introductions
  • Bibliography
• About
  • Authors
  • Citation
  • Contact

SetPoints

Represents collections of points with methods for:

• Random generation (uniform, normal, Poisson processes, clusters)

• Geometric transformations (rotation, scaling, translation, perturbation)

• Visualization

GeometricGraph

Base class for graphs embedded in geometric space with:

• Graph construction and manipulation

• Set operations (union, intersection, difference)

• Property analysis (entropy, orientation, lengths)

• Conversion to GeoPandas for GIS workflows

ProximityGraph

Specialized geometric graphs based on proximity relationships:

• Delaunay Triangulation - Fundamental triangulation structure

• Convex Hull - Boundary of point sets

• MST (Minimum Spanning Tree) - Minimum cost connected graph

• Gabriel Graph - beta-skeleton with beta=1

• RNG (Relative Neighborhood Graph) - beta-skeleton with beta=2

• beta-Skeleton - Parameterized family of proximity graphs

• Unit Disk Graph - Distance-based connectivity

• Sphere of Influence Graph - Based on nearest neighbor spheres

• alpha-Shape - Generalization of convex hull

• alpha-Hull - Hull with circular arcs

• gamma-Neighborhood Graph - Veltkamp’s generalized proximity graph

• Elliptic Gabriel Graph - Gabriel graph with elliptical regions

• sigma-Graph - Scaled distance-based graph

• Stepping Stone Graph - Power-distance based connectivity

Getting Started

from proximitygraphs.points import SetPoints
from proximitygraphs.proximitygraphs import DelaunayG, GG, RNG

# Generate points
points = SetPoints.uniform_square(n=100, dims=2, seed=42)

# Create graphs
delaunay = DelaunayG(points)
gabriel = GG(points)
rng = RNG(points)

# Visualize
gabriel.draw(figsize=(10, 10))

See individual documentation files for detailed information on each class and method.