exo-hypergraph

Hypergraph substrate for higher-order relational reasoning with persistent homology and sheaf theory. Enables cognitive representations that go beyond pairwise edges to capture n-ary relationships natively.

Features

• Hyperedge storage -- first-class support for edges that connect arbitrary sets of nodes, stored in a compressed sparse format.
• Sheaf sections -- attach typed data (sections) to nodes and edges with consistency conditions enforced by sheaf restriction maps.
• Sparse persistent homology (PPR-based O(n/epsilon)) -- computes topological features efficiently using personalised PageRank sparsification.
• Betti number computation -- extracts Betti-0 (connected components), Betti-1 (loops), and higher Betti numbers to summarise structural topology.

Quick Start

Add the dependency to your Cargo.toml:

[dependencies]
exo-hypergraph = "0.1"

Basic usage:

use exo_hypergraph::{HypergraphSubstrate, HypergraphConfig};
use exo_core::{EntityId, Relation, RelationType};

let config = HypergraphConfig::default();
let mut hg = HypergraphSubstrate::new(config);

let e1 = EntityId::new();
let e2 = EntityId::new();
let e3 = EntityId::new();

// Create a 3-way hyperedge
let relation = Relation {
    relation_type: RelationType::new("collaboration"),
    properties: serde_json::json!({"project": "EXO-AI"}),
};
hg.create_hyperedge(&[e1, e2, e3], &relation).unwrap();

// Compute topological invariants
let betti = hg.betti_numbers(2);
println!("Betti numbers: {:?}", betti);

Crate Layout

Requirements

• Rust 1.78+
• Depends on exo-core

Links

• GitHub
• EXO-AI Documentation

License

MIT OR Apache-2.0