IntelligenceFebruary 12, 202648 min read

Graph RAG for Causal Structure Extraction: Matrix Methods for Multi-Hop Retrieval with Evidence Cohesion

How organizational knowledge graphs enable responsibility chain tracing and risk concentration detection

Standard RAG often retrieves flat document chunks that under-represent relational structure needed for causal and responsibility reasoning. Graph RAG models documents and entities as nodes in an adjacency matrix, enabling multi-hop retrieval along causal paths in organizational knowledge. We formalize an h-hop diffusion score, derive hop-depth choices from a noise-accuracy tradeoff, and introduce an evidence-cohesion metric that gates response generation by subgraph density. In contract-corpus evaluations, the method reported 73.4% causal-path extraction accuracy at 3 hops, a 31% improvement over flat Top-k RAG for responsibility-chain identification, and `r = 0.87` correlation between cohesion score and response correctness.

graph-ragcausal-inferenceknowledge-graphsmatrix-methodsevidence-cohesionmulti-hop
MathematicsJanuary 16, 202626 min read

Graph RAG Matrix Modeling and Stable Hop Count Derivation

Spectral analysis of adjacency matrices reveals the optimal diffusion depth that maximizes signal-to-noise ratio in knowledge graph retrieval

Graph-based Retrieval Augmented Generation traverses knowledge graphs to gather context for language-model prompts. Each additional hop `h` in `A^h` can add useful context but also amplify noise through irrelevant paths. This paper models diffusion as matrix exponentiation with decay, derives signal-to-noise behavior by hop count using spectral decomposition, and identifies an optimal hop count `h*`. Across four enterprise knowledge graphs, the derived `h*` reduced hallucination rate by 43% versus fixed-depth traversal.

graph-ragspectral-analysisadjacency-matrixhop-countsignal-to-noiseknowledge-graph