r-irbe Graph Theory & Knowledge Graph Mathematics
Graph-theoretic and knowledge representation foundations for provenance chains, trust networks, knowledge lifecycles, and causal reasoning structures.
Routing
- USE FOR: Graph theory, knowledge graphs, ontology engineering, provenance structures, network analysis, and formal knowledge representation. Use for mathematical reasoning about DAGs, KGs, trust networks, provenance chains, and any graph-structured knowledge. Covers both pure graph theory and applied knowledge graph methodology.
- DO NOT USE FOR: KRR / symbolic AI (use @ai-symbolic-neuro); causal DAGs (use @ai-causal-deontic); discrete math (use @lean-math-discrete).
- TRIGGERS: graph theory, knowledge graph, ontology, provenance, network analysis, formal knowledge representation.
Workflow
- Classify the graph object: directed / undirected / weighted / hypergraph / knowledge-graph / ontology-graph.
- Pick the matching section (graph algorithms, KR semantics, provenance, network metrics).
- Produce the answer; reference the relevant Mathlib
SimpleGraph/Graph/Quivernamespaces. - Hand off: to
@lean-math-discretefor Lean proof, to@lean-knowledge-formalizationfor ontology encoding, to@lean-zettelkasten.
Recovery & STOP
- STOP if KRR/symbolic AI methodology dominates — delegate to
@ai-symbolic-neuro. - STOP if causal-DAG semantics dominate — delegate to
@ai-causal-deontic. - STOP if a pin-verified Mathlib construction is required — escalate to
@lean-research.
Handoffs
- Predecessors:
agent:gateway,skill:lean-research. - Successors:
skill:lean-math-discrete,skill:lean-knowledge-formalization,skill:lean-zettelkasten.
Detailed reference
Full content for math-graph-knowledge lives in
references/math-graph-knowledge-handbook.md.
Load that file when the skill is convened; the SKILL.md only carries
the dispatch contract and the parts index.
| Section | Topic |
|---|---|
| Part 1 | Graph Theory Foundations |
| Part 2 | Knowledge Graph Theory |
| Part 3 | Provenance Mathematics |
| Part 4 | Network Analysis for Knowledge Structures |
| Part 5 | Ontology Engineering |
| Part 6 | Causal Graph Theory |
| Part 7 | Formalization Entry Points |
See also
../../references/math-graph-knowledge-handbook.md— Full handbook (extracted from this skill)../lean-math-discrete/SKILL.md— Successor../lean-knowledge-formalization/SKILL.md— Successor../lean-zettelkasten/SKILL.md— Successor