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PageRank is one of several interesting centrality metrics that could be applied to a graph to influence RAG on structural data, another one is Triangle Centrality which counts triangles around nodes to figure out their centrality based on the concept that triangles close relationships into a strong bond, where open bonds dilute centrality by drawing weight away from the center:

https://arxiv.org/abs/2105.00110

The paper shows high efficiency compared to other centralities like PageRank, however in some research using the GraphBLAS I and my coauthors found that TC was slower on a variety of sparse graphs than our sparse formulation of PR for graphs up to 1.8 billion edges, but that TC appears to scale better as graphs get larger and is likely more efficient in the trillion edge realm.

https://fossies.org/linux/SuiteSparse/GraphBLAS/Doc/The_Grap...

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liukidar 7 days ago | parent | next [-]

This is super interesting! Thanks for sharing. Here we are talking of graphs in the milions nodes/edges, so efficiency is not that big of a deal, since anyway things are gonna be parsed by a LLM to craft an asnwer which will always be the bottleneck. Indeed PageRank is the first step, but we would be happy to test more accurate alternatives. Importantly, we are using personalized pagerank here, meaning we give specific intial weights to a set (potentially quite large) of nodes, would TC support that (as well as giving weight to edges, since we are also looking into that)?

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michelpp 6 days ago | parent [-]

> Here we are talking of graphs in the milions nodes/edges,

That ought to be enough for anybody.

> would TC support that

TC is a purely structural algorithm, it counts triangles so it doesn't take any weights into consideration, but it does return a vector of normalized ranking from 0.0 to 1.0, which you could combine with an existing biasing strategy to boost results that have strong centrality.

	▲	lmeyerov 6 days ago \| parent [-]
		Hah indeed, we are doing billion-scale real-time graph rag in louie.ai for fairly regular tasks, so your sentiment resonates ;-) For something like uploading a big folder of documents, agree with the OP, pretty straightforward, naive in-memory with out-of-the-box embeddings, LLMs, retrieval, and untuned DBs goes far. I expect most vector-supporting dbaas and LLMaaS to be offering in the new year. OpenAI, Claude, and friends are already going in this direction, leaving the rag techniques opaque for now. (Something folks may not appreciate, and I think is important about what's being done here, is the incremental update aspect.)

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arkokoley 7 days ago | parent | prev [-]

Have you tried Authority Rank as a substitute for PageRank? https://link.springer.com/content/pdf/10.1007/978-3-030-6097...