← Back to article

Equation 19 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

What does this equation mean?

QQ

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

the when. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

QQ

Symbol Q

the when.

Understand this part →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

When Q is small — a corpus queried rarely, or one still being explored — CindexC_{\text{index}} dominates and the naive or hybrid architectures are cheaper by a wide margin, because they pay nothing until a query arrives. When Q is large against a stable corpus, the fixed term is driven down toward zero and the comparison turns on cmarginalc_{\text{marginal}} against the per-query cost of the alternatives. The direction of that comparison depends on the question being asked, not only on volume: Edge and colleagues report that GraphRAG produces substantially more comprehensive and diverse answers than a conventional RAG baseline specifically on query-focused summarisation over large corpora, the kind of…
Read the full surrounding passage
When Q is small — a corpus queried rarely, or one still being explored — CindexC_{\text{index}} dominates and the naive or hybrid architectures are cheaper by a wide margin, because they pay nothing until a query arrives. When Q is large against a stable corpus, the fixed term is driven down toward zero and the comparison turns on cmarginalc_{\text{marginal}} against the per-query cost of the alternatives. The direction of that comparison depends on the question being asked, not only on volume: Edge and colleagues report that GraphRAG produces substantially more comprehensive and diverse answers than a conventional RAG baseline specifically on query-focused summarisation over large corpora, the kind of question — “what are the main themes across this entire collection” — that a top- k chunk retriever structurally cannot answer well no matter how many times it is queried, because no fixed small set of chunks represents a corpus-wide theme [ 4 ] .

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Browse the mathematical compendium →