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Equation 18 · Part 2 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Symbol Q

cquery(Q)=CindexQ+cmarginal.c_{\text{query}}(Q) = \frac{C_{\text{index}}}{Q} + c_{\text{marginal}}.
QQ

What this part means

the when.

Its job in the formula

Q occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Where the article explains it

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.

The passage around this formula

…for the one-time cost of building the graph and its community summaries, and cmarginalc_{\text{marginal}} for the cost of answering a single query against the finished structure, the amortised cost of a query workload of size Q against one graph is cquery(Q)=CindexQ+cmarginalc_{\text{query}}(Q) = \frac{C_{\text{index}}}{Q} + c_{\text{marginal}}. 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…

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Sources cited in the surrounding passage

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