Graph center
set of all vertices of minimum eccentricity
The center (or Jordan center) of a graph is the set of all vertices of minimum eccentricity, that is, the set of all vertices u where the greatest distance d(u,v) to other vertices v is minimal. Equivalently, it is the set of vertices with eccentricity equal to the graph's radius. Thus vertices in the center (central points) minimize the maximal distance from other points in the graph.
This is also known as the vertex 1-center problem and can be extended to the vertex k-center problem.
Finding the center of a graph is useful in facility location problems where the goal is to minimize the worst-case distance to the facility. For example, placing a hospital at a central point reduces the longest distance the ambulance has to travel.
The center can be found using the Floyd–Warshall algorithm. Another algorithm has been proposed based on matrix calculus.
The concept of the center of a graph is related to the closeness centrality measure in social network analysis, which is the reciprocal of the mean of the distances d(A,B).
This brief starts where responsible research should: with the source description of “Graph center” as set of all vertices of minimum eccentricity. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as set of all vertices of minimum eccentricity. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Oct 16, 2023. The linked authority identifier is Q5597075. None of the 0 selected statements returned an explicit reference.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Graph center”, its source revision and the description used here.
- Expand the search: follow Graph center primary sources, Graph center archive and Graph research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Graph center”?
- Which cited source is closest to the event, object or claim?
- What terminology or title could unlock a more precise catalogue search?
Search terms from this dossier
This entry incorporates text from “Graph center” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.