The Erdős number is a simple integer-valued measure of collaborative distance in academic authorship, named after the Hungarian mathematician Paul Erdős. It records the length of the shortest chain of coauthored research papers that connects a given author to Erdős. The concept both commemorates Erdős's extraordinary collaborative output and provides a playful indicator of connectedness within the mathematical literature.
Definition and calculation
By definition, Paul Erdős himself has Erdős number 0. Any researcher who coauthored a paper with Erdős has Erdős number 1. A scholar who has not written with Erdős but has coauthored with at least one person with Erdős number 1 is assigned Erdős number 2, and so on. Practically, these distances are found by searching bibliographic databases and forming a coauthorship graph, then computing shortest paths from Erdős to the target author.
Typical rules and conventions
- Only scholarly publications with formal coauthorship are counted; acknowledgements or informal collaborations do not establish an edge.
- Edges normally represent joint authorship of articles, books, or conference papers indexed by a bibliographic service.
- Different databases may give different answers because of coverage, spelling variants, and author disambiguation.
History and significance
The notion grew from mathematicians' awareness of Paul Erdős's prolific coauthoring habits and circulated informally before being tabulated in online resources. It exemplifies the small-world phenomenon in scholarly networks: because Erdős collaborated with many people across subfields, a large fraction of active mathematicians have small Erdős numbers. The idea has inspired comparable measures in other domains, for example film actors' Bacon numbers, and combined metrics like the Erdős–Bacon number for people active in both science and entertainment.
Uses, examples, and caveats
Researchers sometimes quote their Erdős number for fun or as an anecdote about connectivity. Professional uses include informal studies of collaboration patterns and network structure. Care must be taken when interpreting these numbers: they reflect only coauthorship in indexed literature, are sensitive to database errors, and carry no direct measure of scientific impact. For general reference or to check a specific name, consult bibliographic services or curated lists; see an example profile of Erdős at Paul Erdős profile and related resources at collaboration databases.
Notable fact: although playful, the Erdős number highlights how collaboration networks link diverse researchers and illustrates graph-theoretic ideas in an accessible setting.