Harmonic Centrality
noun

Definition:
A score that measures how close your website, page, or entity is to the rest of the web, based on link distance rather than link count.

Usage:

“After running a link building campaign our Harmonic Centrality score greatly improved and we began appearing more in ChatGPT recommendations.”

“Improving harmonic centrality means reducing the number of link steps between your content and the rest of the web, making your brand mathematically closer to the knowledge networks that train and power modern AI search.”

Explanation:
Harmonic Centrality in SEO or AI SEO terms is a measure of how quickly a domain, document URL, or entity can be reached from the web as a whole, a specific topical cluster on the web, or a trust weighted segment of a topical cluster on the web.

It differs from Google’s PageRank in that it does not directly take into account the value of a page or URL and that it can be applied to entities without the need for hypertext links.

There is as of yet no evidence or admissions that any major search engines or LLM systems use harmonic centrality scoring systems for their rankings. The only system explicitly known to use harmonic centrality is Common Crawl. However, given the nature of harmonic centrality and other centrality scoring mathematical systems in information retrieval, it is highly plausible that such systems have at least been experimented with if not silently implemented.

Compare:
PageRank, Topical Authority, Domain Authority, Domain Rank, Domain Rating, Page Authority, Trust Flow

History:
Harmonic Centrality was introduced to the SEO / AI SEO world by Common Crawl, a company that compiles a dataset of the open web for LLM models to use in their training data (ChatGPT, Claude, Copilot, Grok, Gemini, Meta AI, etc…). However, the mathematics were created in the early 2000’s by network physicists Vito Latora and Massimo Marchiori in their 2001 paper “Efficient Behavior of Small-World Networks”

Resources:
“Axioms of Centrality” by Professor Paolo Boldi and Sebastiano Vigna of University of Milan published on March 29th, 2020: https://vigna.di.unimi.it/ftp/papers/AxiomsForCentrality.pdf

“Common Crawl’s First In-House Web Graph” by Distinguished Engineer at Common Crawl Sebastian Nagel published on May 22nd, 2017: https://web.archive.org/web/20251218084236/https://commoncrawl.org/blog/hostgraph-2017-feb-mar-apr-crawls

“Efficient Behavior of Small-World Networks” by Vito Latora and Massimo Marchiori published on January 25th, 2001: https://arxiv.org/abs/cond-mat/0101396

“Harmonic Centrality vs. PageRank: Taking a Deeper Dive” by Dawn Anderson for Search Engine Journal published on January 24th, 2019: https://www.searchenginejournal.com/harmonic-centrality-vs-pagerank-deep-dive/288139/

X thread by “Metehan Yesilyurt”: https://x.com/metehan777/status/2008899533757993276