BlockCutpointGraph - getBlock

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BlockCutpointGraph - getBlock

Carl Witt
Hello JGraphT Users,

I have a question concerning the public UndirectedGraph<V,E> getBlock(V vertex) method.
The documentation says

    Returns the vertex if vertex is a cutpoint, and otherwise returns the block (biconnected component) containing the vertex.


But the example given in the introductory section of the BlockCutpointGraph class clarifies that the a vertex can be part of more than one block

    http://mathworld.wolfram.com/Block.html

Is the documentation of the getBlock method being imprecise (should it read "returns a block containing the vertex") or is the underlying definition of a block not the one from Mathworld?

Best regards,
Carl Witt


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Re: BlockCutpointGraph - getBlock

H.N. de Ridder
On Fri, Nov 29, 2013 at 04:06:48PM +0100, Carl Witt wrote:

Hello Carl,

> I have a question concerning the public UndirectedGraph
> <http://jgrapht.org/javadoc/org/jgrapht/UndirectedGraph.html><V
> <http://jgrapht.org/javadoc/org/jgrapht/alg/BlockCutpointGraph.html>,E
> <http://jgrapht.org/javadoc/org/jgrapht/alg/BlockCutpointGraph.html>>
> *getBlock*(V
> <http://jgrapht.org/javadoc/org/jgrapht/alg/BlockCutpointGraph.html> vertex)
> method.
> The documentation says
>
>      Returns the vertex if vertex is a cutpoint, and otherwise returns
> the block (biconnected component) containing the vertex.
>
> But the example given in the introductory section of the
> BlockCutpointGraph class clarifies that the a vertex can be part of more
> than one block
>
> Is the documentation of the getBlock method being imprecise (should it
> read "returns a block containing the vertex") or is the underlying
> definition of a block not the one from Mathworld?

I don't know how it could happen, but cutpoint is one of the very few
concepts in graph theory that have only one meaning. A cutpoint is indeed in
more than one block (x is a cutpoint iff x is in more than one block), but
non-cutpoints are in precisely one block.

So getBlock(x) returns x if x is a cutpoint and the unique block that
contains x, otherwise.

Hope this clears things up,
   Ernst

--
Information System on Graph Classes and their Inclusions (ISGCI)
http://www.graphclasses.org

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