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Equation 18 · Part 3 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Symbol C_index

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

What this part means

the writing.

Its job in the formula

CiC_index occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

Writing CindexC_{\text{index}} 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}}.

The passage around this formula

This is the one family among the five whose defining engineering trade-off is temporal rather than architectural: cost is shifted from query time to index time. Writing CindexC_{\text{index}} 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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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