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Equation 20 · Part 1 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Symbol C_index

CindexC_{\text{index}}
CindexC_{\text{index}}

What this part means

the writing.

Its job in the formula

CiC_index is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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

The passage around this formula

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…

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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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