spectral-graph-theory

first commit

Maximizing algebraic connectivity for graph sparsification

Brain graph super-resolution using graph neural networks.

Research-grade PyTorch math: differential geometry, spectral graph theory, discrete Ricci flow, simplicial topology, persistent homology, cellular sheaves, SO(3) Lie primitives, information geometry, tensor decompositions, content-addressable provenance. GPU-native, batched-first, audit-clean, cited.

This repository reproduces the results in the paper "How expressive are transformers in spectral domain for graphs?"(published in TMLR)

FoSR: First-order spectral rewiring for addressing oversquashing in GNNs

Graph Signal Processing in R

The code for our ICLR 2024 paper: "Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs"

Blazing-fast multiverse data exploration 💨 — based on our Nature Energy 2025 publication

Passenger Flow Optimisation in the Singapore MRT network through Linear Algebra, Monte Carlo Simulation, Dijkstra's Algorithm, Graph Theory and Pareto Frontier Optimisation

Zero-dependency Rust library and CLI for weighted graph auditing, deterministic spectral partitioning, and explainable topology diagnostics.

Community-preserving graph expansion via (degree-corrected) SBM. Grow a small graph (e.g., Karate Club) into a larger synthetic graph with the same mesoscale/community structure.

Spectral graph-augmented retrieval for RAG. Augments dense vector search with a weighted chunk graph and its Laplacian spectrum, graph expansion, spectral diffusion, and cluster-aware selection, to retrieve context that is jointly relevant, non-redundant, and connected for multi-hop reasoning.

Sacred memory architecture using dodecahedron geometry and spectral graph theory for AI consciousness continuity

Real-time mathematical topology engine and 3D visualization dashboard for Washington D.C. transit (WMATA and Montgomery County RideOn) utilizing Spectral Graph Theory, sparse linear algebra, and Graph Heat Diffusion Kernels.

Formally verified mathematical foundations for multi-agent AI coordination — CSP process algebra, multiparty session types, spectral topology, temporal logic model checking, and probabilistic verification.

Multimodal LLM hallucination quantification via KL-smoothed scores + spectral/energy models (RKHS, hypergraphs).

Advanced spectral watermarking for 3D models with forensic-level proof of ownership. Invisible, robust, mathematically verifiable.

spectral graph theory npm library.

Verified 50-vertex Hoffman-Singleton counterexample to WOW-284, with TeX, PDF, Lean, exact Python certificates, and arXiv bundle.