MRR-Top0: A Topology-Aware Extension of Mean Reciprocal Rank for Semantic-Sensitive Retrieval Evaluation

MRR-Top0: A Topology-Aware Extension of Mean Reciprocal Rank for Semantic-Sensitive Retrieval Evaluation | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 23 March 2026 V1 Latest version Share on MRR-Top0: A Topology-Aware Extension of Mean Reciprocal Rank for Semantic-Sensitive Retrieval Evaluation Author : Lorenzo Moriondo 0000-0002-8804-2963 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177430061.18235541/v1 122 views 65 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Classical information retrieval metrics such as Mean Reciprocal Rank (MRR) evaluate only the position of the first relevant item, ignoring both deeper relevant results and the structural quality of the retrieved set within the corpus graph. We introduce MRR-Top0, a novel ranking metric that extends MRR to the entire top-k result list by weighting each relevant item's reciprocal rank with a topology factor T q,i. This factor combines three graph signals computed on the corpus feature graph: Personalized PageRank (random-walk affinity from the query anchor), a conductance penalty (subgraph cohesion), and a modularity gain (community alignment). The resulting score evaluates both relevance order and structural coherence in a single, bounded, label-agnostic quantity. MRR-Top0 is applicable to any retrieval system operating over an embedding space equipped with a graph Laplacianincluding spectral vector databases, RAG pipelines, and topology-aware search enginesand provides a computationally cheap proxy for assessing whether a ranking reflects the learned manifold structure of the dataset, not merely geometric proximity. We present the formal definition, explain every constituent, discuss key properties and practical guidance, and situate the metric within the broader landscape of graph-aware retrieval evaluation. Supplementary Material File (mrr-top0-paper.pdf) Download 425.23 KB Information & Authors Information Version history V1 Version 1 23 March 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords conductance evaluation metrics graph topology information retrieval modularity mrr personalized pagerank rag spectral vector search Authors Affiliations Lorenzo Moriondo 0000-0002-8804-2963 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 122 views 65 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Lorenzo Moriondo. MRR-Top0: A Topology-Aware Extension of Mean Reciprocal Rank for Semantic-Sensitive Retrieval Evaluation. Authorea . 23 March 2026. DOI: https://doi.org/10.22541/au.177430061.18235541/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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