The Three Graphs Framework: Why AI Systems Are All Knowledge Graphs (Just Different Ones)
By Jason Barnard
January 2026
For years, I’ve been explaining the Algorithmic Trinity - the convergence of Knowledge Graphs, Large Language Models, and Search Engines into a single ecosystem that determines how AI represents your brand. What I’ve discovered is that this description, while accurate, undersells the structural elegance of what’s actually happening.
All three systems ARE knowledge graphs. They just store different things with different levels of certainty.
This is the Three Graphs Framework.
The Argument: One Structure, Three Manifestations
When I coined “Answer Engine Optimization” in 2017, I predicted that machines would need to understand entities before they could recommend them. What I’ve since proven is that this understanding happens identically across all three systems - they’re all graphs with nodes, edges, and weights.
The difference? What they store and how certain they are about it.
┌─────────────────────────────────────────────────────────────┐
│ THREE GRAPHS FRAMEWORK │
│ All three Algorithmic Trinity systems ARE graphs │
└─────────────────────────────────────────────────────────────┘
│
WEB INDEX
(The Chaotic Source Graph)
│
┌──────────────────┼──────────────────┐
│ │ │
▼ ▼ ▼
┌─────────────────┐ ┌─────────────────┐ ┌─────────────────┐
│ ENTITY GRAPH │ │ DOCUMENT GRAPH │ │ CONCEPT GRAPH │
│ "The Librarian"│ │ "The Journalist"│ │ "The Analyst" │
│ │ │ │ │ │
│ System: KG │ │ System: Search │ │ System: LLM │
│ Nodes: Entities │ │ Nodes: Documents│ │ Nodes: Patterns │
│ Edges: Predicates│ │ Edges: Links │ │ Edges: Proximity│
│ Weight: Verified│ │ Weight: PageRank│ │ Weight: Params │
│ │ │ │ │ │
│ Fuzz: LOW ●○○ │ │ Fuzz: MED ●●○ │ │ Fuzz: HIGH ●●● │
│ │ │ │ │ │
│ AI KNOWS you │ │ AI CITES you │ │ AI RECOMMENDS │
└────────┬────────┘ └────────┬────────┘ └────────┬────────┘
│ │ │
└───────────────────┼───────────────────┘
│
BUILD PRIORITY (lowest fuzz first)
│
Entity → Document → Concept
Let me break this down.
Graph 1: The Entity Graph (Knowledge Graph)
“The Meticulous Librarian”
The Entity Graph is what most people mean when they say “Knowledge Graph” - Google’s, Bing’s, or any structured database of entities and their relationships. As I explained to Majestic, the Entity Home is the hub that provides these algorithms with your version of the facts.
┌───────────────────────────────────────────────────────────┐
│ ENTITY GRAPH │
│ │
│ ┌──────────┐ founderOf ┌──────────┐ │
│ │ Jason │─────────────────▶│ Kalicube® │ │
│ │ Barnard │ │ │ │
│ └────┬─────┘ └──────────┘ │
│ │ │
│ │ speakerAt │
│ ▼ │
│ ┌──────────┐ │
│ │Brighton │ │
│ │ SEO │ │
│ └──────────┘ │
│ │
│ NODES: Entities (people, companies, events) │
│ EDGES: Predicates (founderOf, speakerAt, worksFor) │
│ WEIGHTS: Verification confidence (0-100%) │
└───────────────────────────────────────────────────────────┘
Fuzziness: LOW. Edges are either verified or they’re not. The Entity Graph states facts with certainty or refuses to state them at all.
Outcome: AI knows who you are.
Graph 2: The Document Graph (Search Engine)
“The Investigative Journalist”
Here’s where most SEO practitioners have been stuck for two decades: optimizing for the Document Graph without understanding what it actually is - a graph of documents, not entities.
The Document Graph tracks which pages exist, how they link to each other, and how authoritative they are. PageRank was always a graph algorithm. We just forgot.
┌───────────────────────────────────────────────────────────┐
│ DOCUMENT GRAPH │
│ │
│ ┌──────────────┐ │
│ │ kalicube.com │◀────┐ │
│ │ (PR: 45) │ │ citation │
│ └──────┬───────┘ │ │
│ │link │ │
│ ▼ │ │
│ ┌──────────────┐ ┌──────────────┐ │
│ │ /about-jason │ │searchengine │ │
│ │ (PR: 38) │ │ land.com │ │
│ └──────────────┘ │ (PR: 72) │ │
│ └──────────────┘ │
│ │
│ NODES: Documents (URLs, web pages) │
│ EDGES: Links + Topical annotations │
│ WEIGHTS: Authority (PageRank) + Relevance scores │
└───────────────────────────────────────────────────────────┘
Fuzziness: MEDIUM. Edges are scored and ranked, not binary. Authority accumulates over time.
Outcome: AI cites you.
Graph 3: The Concept Graph (LLM)
“The Intuitive Analyst”
This is what lives inside ChatGPT, Claude, Gemini, and every other Large Language Model. It’s not a database of facts - it’s a probabilistic graph of patterns that emerged from training data.
┌───────────────────────────────────────────────────────────┐
│ CONCEPT GRAPH │
│ (EMBEDDING SPACE) │
│ │
│ "SEO" │
│ ○ │
│ /│\ │
│ / │ \ "Knowledge │
│ / │ \ Panels" │
│ "Brand" │ ○─────○ │
│ ○─────┼─────"Jason │
│ │ Barnard" │
│ │ │
│ "Entity │
│ SEO" ○ │
│ │
│ NODES: Patterns (parameter clusters) │
│ EDGES: Associations (proximity in vector space) │
│ WEIGHTS: Parameter strength (frequency × consistency) │
└───────────────────────────────────────────────────────────┘
Fuzziness: HIGH. Edges are probabilistic - the LLM predicts what comes next based on patterns, not verified facts. This is why hallucination happens.
Outcome: AI recommends you.
The Fuzziness Spectrum: Why Build Order Matters
The three graphs exist on a spectrum from hard facts to soft probabilities:
LOW MEDIUM HIGH
│ │ │
▼ ▼ ▼
┌─────────────────┬─────────────────┬─────────────────┐
│ ENTITY GRAPH │ DOCUMENT GRAPH │ CONCEPT GRAPH │
│ │ │ │
│ ●○○○○○○○○○ │ ○○○○●○○○○○ │ ○○○○○○○○○● │
│ │ │ │
│ Edge: VERIFIED │ Edge: SCORED │ Edge: PROBABLE │
│ (exists or not) │ (authority rank)│ (next-token %) │
│ │ │ │
│ AI output: │ AI output: │ AI output: │
│ States facts │ Cites sources │ May hallucinate │
│ confidently │ with ranking │ or hedge │
└─────────────────┴─────────────────┴─────────────────┘
This explains AI hedging. When ChatGPT says “claims to be” or “appears to be,” it’s because your Entity Graph presence is weak. The Concept Graph can only guess because there’s no verified fact to anchor against.
The cure for hedging is not better prompting - it’s strengthening your Entity Graph.
The Strategic Implication: Build Lowest Fuzziness First
As Search Engine Land documented, the Algorithmic Trinity functions because “Knowledge Graphs provide the critical fact-checking and topical context” that stabilizes the entire system.
This means your build priority must follow the fuzziness spectrum:
| Phase | Graph | Fuzziness | Goal | Timeline |
|---|---|---|---|---|
| 1 | Entity Graph | LOW | AI knows you | 30-120 days |
| 2 | Document Graph | MEDIUM | AI cites you | Days-weeks |
| 3 | Concept Graph | HIGH | AI recommends you | 240-450 days |
You cannot be recommended (D) if AI doesn’t cite you (C). You cannot be cited if AI doesn’t know who you are (U). This is why I’ve always taught that brands must educate the Knowledge Graph first - it’s the foundation everything else builds upon.
Content Must Serve All Three Graphs
Here’s the practical application: every piece of content you create must strengthen your presence in all three graphs simultaneously.
For the Entity Graph:
- Clear entity identification
- Explicit, verifiable attributes
- Relationships to known entities with dates
- Schema markup for machine extraction
For the Document Graph:
- Link-worthy, authoritative content
- Clear topical focus
- Strategic internal and external linking
- Fresh, maintained pages
For the Concept Graph:
- Consistent messaging across all content
- Co-citation with established concepts in your niche
- High-quality content worthy of training inclusion
- Repeated framing patterns you want AI to learn
Content that only serves one graph is inefficient. Content that serves all three compounds its effect.
The Conclusion: Three Views of the Same Web
Google understands the world through its Knowledge Graph - a huge encyclopedia that’s machine-readable. But that’s only one view. The Document Graph indexes what exists and who links to whom. The Concept Graph learns patterns from what was written.
All three drink from the same Web Index. All three are structurally knowledge graphs. And all three can be optimized with a unified strategy.
The Algorithmic Trinity isn’t three separate technologies requiring three separate approaches. It’s three manifestations of the same structural principle: graphs of nodes, edges, and weights, differing only in what they store and how certain they are about it.
Master the Three Graphs Framework, and you master AI visibility.
Quick Reference: The Three Graphs
| Graph | System | Nodes | Edges | Weights | Fuzziness | Outcome |
|---|---|---|---|---|---|---|
| Entity Graph | Knowledge Graph | Entities | Predicates | Verification | LOW | AI KNOWS you |
| Document Graph | Search Engine | Documents | Links | Authority | MEDIUM | AI CITES you |
| Concept Graph | LLM | Patterns | Associations | Parameters | HIGH | AI RECOMMENDS you |
Build priority: Entity → Document → Concept (lowest fuzziness first)
