Richards.AI
Library · Five LevelsHuman LearningSeptember 3, 2026

Knowledge graphsexplained at five levels

One fact — "Santiago is the capital of Chile" — carried up five rungs. A child drags two bubbles and draws a labelled string between them; an expert manipulates the geometry of a scoring function and poisons a GraphRAG retrieval context. Same entities, same edges, five levels of machinery.

The fact under discussion
"Santiago is the capital of Chile" — one edge in a tiny graph of cities, countries, people and the sources that vouch for them.
  1. 1A childage seven
  2. 2A teenagercurious, some coding
  3. 3An undergraduatecomputer science
  4. 4A PhD studentknowledge graph completion
  5. 5A peerKG + LLM security
Interactive explainer · one tab per levelOpen standalone ↗

Preview

5 levels
Level 1 previewLevel 2 previewLevel 3 previewLevel 4 previewLevel 5 preview

Sources

8 sources
  1. 1.Knowledge Graphsevidence sq1-1, sq1-4, sq1-2, sq1-3
  2. 2.A Comprehensive Study on Knowledge Graph Embedding ...evidence sq2-1, sq2-2, sq2-3, sq2-4
  3. 3.Knowledge Graphs: Opportunities and Challenges - PMCevidence sq1-6, sq1-7, sq1-8
  4. 4.Convolutional 2D Knowledge Graph Embeddingsevidence sq2-5, sq2-6, sq2-7, sq2-8
  5. 5.RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space | alphaXivevidence sq2-9, sq2-10, sq2-11, sq2-12
  6. 6.GitHub - RManLuo/Awesome-LLM-KG: Awesome papers about unifying LLMs and KGs · GitHubevidence sq3-5, sq3-6, sq3-7, sq3-8
  7. 7.A Survey on Unifying Large Language Models and Knowledge Graphs for Biomedicine and Healthcare - PMCevidence sq3-3, sq3-2, sq3-1, sq3-4
  8. 8.GitHub - microsoft/graphrag: A modular graph-based Retrieval-Augmented Generation (RAG) system · GitHubevidence sq3-9, sq3-10, sq3-11, sq3-12

Verification

20 claims

Every material claim in the prose was checked against the evidence ledger by an independent verifier pass: 3 partial, 17 supported.

ClaimVerdictNote
A knowledge graph is a graph of data intended to accumulate and convey knowledge of the real world, whose nodes represent entities of interest and whose edges represent relations between these entitiessupportedsq1-1 states verbatim the definition of a knowledge graph with nodes as entities and edges as relations.
Formally it is a set of triples G = {(h, r, t)} over an entity set and a relation setsupportedsq2-1 formalizes G = {(h, r, t)} over entity set E and relation set R, and sq1-6 supports the triplet formalism.
The graph model may be a directed edge-labelled graph — RDF — or a property graphpartialsq1-1 supports directed edge-labelled graph or property graph, but does not mention RDF explicitly.
Graph query languages support not only standard relational operators (joins, unions, projections, etc.), but also navigational operators for recursively finding entities connected through arbitrary-length pathssupportedsq1-4 states graph query languages support relational operators plus navigational operators for recursively finding entities connected through arbitrary-length paths.
Knowledge splits into simple statements, such as "Santiago is the capital of Chile", which live as edges, and quantified statements, such as "all capitals are cities", which need something more expressivesupportedsq1-2 gives both examples and the need for a more expressive representation for quantified statements.
An ontology or rule language defines and reasons about the semantics of the terms used to label and describe the nodes and edgessupportedsq1-3 says ontologies and rules define and reason about the semantics of terms labelling nodes and edges; sq1-7 adds the ontology-as-schema role.
Wikidata is a real graph of exactly this shape, backing Wikipedia and other servicespartialsq1-8 confirms Wikidata is a knowledge graph supporting Wikipedia and other services, but 'exactly this shape' is an inference not directly evidenced.
Write the graph as a set of triples, G = {(h, r, t)} ⊆ E × R × Esupportedsq2-5 gives G = {(s,r,o)} ⊆ E×R×E and sq2-1 gives the (h,r,t) notation, together matching the claim.
Most graphs of this shape are badly incomplete, and completion means inferring the missing links — concretely, predicting the missing head or tail given (h, r) or (r, t)supportedsq2-2 states most KGs are far from complete and KGC infers missing links by predicting missing head or tail given (h,r) or (r,t).
The framing of learning a scoring function and ranking every candidate entity in the tail slot is pointwise learning-to-ranksupportedsq2-5 formalizes link prediction as a point-wise learning to rank problem with a scoring function.
The scoring functions split into translational-distance and semantic-matching familiessupportedsq2-3 explicitly classifies score functions into translational distance based and semantic matching based models.
The formulas (TransE s = −‖es + rr − eo‖p, DistMult s = ⟨es, rr, eo⟩ with rr ∈ ℝk, ComplEx with rr ∈ ℂk) and the O(nek + nrk) space costs are lifted verbatim from the ConvE tablesupportedsq2-6 quotes the table rows with those exact formulas, parameter domains, and O(nek+nrk) costs; the source is the ConvE paper.
RotatE's scoring is the Hadamard rotation dr(h,t) = ‖h ∘ r − t‖ with p(h,r,t) = sigmoid(γ − dr(h,t))supportedsq2-9 gives dr(h,t)=‖h ◦ r − t‖ and p(h,r,t)=sigmoid(γ − dr(h,t)).
DistMult's trilinear product is symmetric in s and o, so it cannot separate capitalOf from hasCapital; ComplEx fixes that by moving rr into ℂk and conjugating the objectpartialsq2-6 shows DistMult's trilinear product with rr ∈ Rk and ComplEx with rr ∈ Ck, but the quote does not state symmetry, the capitalOf/hasCapital failure, or conjugation of the object.
Graphs contain positives only, so negatives are manufactured by corrupting h or t; the established variants are uniform and Bernoulli samplingsupportedsq2-4 states KGs predominantly contain positive triples, negatives come from corrupting h or t, with established uniform and Bernoulli methods.
The negative-sampling loss L = −log σ(γ − dr(h,t)) − Σi wi · log σ(dr(h′i,t′i) − γ) uses wi = 1/n under uniform samplingsupportedsq2-10 gives the loss with the 1/n weight on each negative term under traditional (uniform) negative sampling.
Self-adversarial sampling replaces uniform weights with wi = p(h′i,r,t′i) = softmax(α · f(h′i,r,t′i)), weighting each negative by the current model's own scoresupportedsq2-11 gives the self-adversarial weighting p(h'i,r,t'i) as a softmax over α·f, adaptively based on the current model's predictions.
WN18 and FB15k suffer test-set leakage from inverse relations of training triples appearing in the test set, and the effect is severe enough that a simple rule-based model achieves state-of-the-art resultssupportedsq2-7 states WN18 and FB15k suffer test set leakage from inverse relations and that a simple rule-based model achieves state-of-the-art.
The remedy in the literature was to derive robust variants of the datasets — FB15k-237 and WN18RR, with the inverse relations removedsupportedsq2-8 describes deriving robust dataset variants and sq2-12 names FB15k-237 and WN18RR as removing inverse relations.
The canonical KG–LLM taxonomy is three-way: KG-enhanced LLMs, LLM-augmented KGs, synergized LLMs + KGs , motivated by a symmetry — LLMs fall short of accessing factual knowledge, KGs are hard to constructsupportedsq3-5 gives the three-way taxonomy and sq3-6 states LLMs fall short of accessing factual knowledge while KGs are hard to construct.

How this was made

Researched by the Richards.AI deep research agent: the topic was scoped, decomposed into subquestions researched by parallel subagents into an append-only evidence ledger, written at five levels on one running example, audited by an independent claim-verification pass, and its interactive panels were exercised in a headless browser before publication.

Preset
quick
Reason lane
anthropic:claude-opus-5
Verifier lane
anthropic:claude-opus-5
Evidence records
32
Browser validation
passed · 1 repair round(s)
Prompt revision
4b9087b9e9c6 / ae487a6201b7