Crate amari_network 

Geometric Network Analysis

This crate provides graph/network analysis tools where nodes are embedded in Clifford algebra (geometric algebra) space. This enables:

• Geometric distance metrics between nodes
• Community detection via geometric clustering
• Information diffusion using geometric products
• Fast path-finding with tropical algebra

Mathematical Foundation

Nodes are represented as multivectors in Cl(P,Q,R), the Clifford algebra with signature (P,Q,R). The geometric distance between nodes uses the natural norm in this space: ||a - b|| where a and b are node positions.

Basic Usage

use amari_network::GeometricNetwork;
use amari_core::Vector;

// Create a network in 3D Euclidean space (signature 3,0,0)
let mut network = GeometricNetwork::<3, 0, 0>::new();

// Add nodes at specific geometric positions
let node1 = network.add_node(Vector::from_components(1.0, 0.0, 0.0).mv);
let node2 = network.add_node(Vector::from_components(0.0, 1.0, 0.0).mv);

// Connect nodes with weighted edges
network.add_edge(node1, node2, 1.0).unwrap();

// Compute geometric properties
let distance = network.geometric_distance(node1, node2);
let centrality = network.compute_geometric_centrality();

Features

• Geometric Embedding: Nodes as multivectors in Clifford algebra space
• Tropical Optimization: Fast path-finding using tropical (max-plus) algebra
• Community Detection: Spectral and geometric clustering methods
• Diffusion Modeling: Information propagation via geometric products
• Centrality Measures: Geometric, betweenness, and eigenvector centrality

Application Areas

• Social network analysis with semantic embeddings
• Citation networks with geometric document representations
• Graph neural networks with geometric features
• Epistemic network analysis
• Belief/information propagation modeling

Re-exports

pub use error::NetworkError;

pub use error::NetworkResult;

Modules

error

Error types for network analysis operations

tropical

Tropical network analysis using max-plus algebra

Structs

Community

Result of community detection analysis

GeometricEdge

Edge with geometric properties

GeometricNetwork

A network where nodes are embedded in geometric algebra space

NodeMetadata

Metadata associated with a network node

PropagationAnalysis

Result of information propagation analysis