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mohawk2 merged 1 commit into from
Mar 27, 2025
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Enhancing documentation for betweenness and for weak connectedness #37

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32 changes: 23 additions & 9 deletions lib/Graph.pod
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Original file line number Diff line number Diff line change
Expand Up @@ -917,7 +917,7 @@ For an undirected graph, return true if the graph is edge-connected
(if it has no bridges).

Note: more precisely, this would be called is_edge_biconnected,
since there is a more general concept of being k-connected.
since there is a more general concept of being k-connected.

=item is_edge_separable

Expand All @@ -927,7 +927,7 @@ For an undirected graph, return true if the graph is edge-separable
(if it has bridges).

Note: more precisely, this would be called is_edge_biseparable,
since there is a more general concept of being k-connected.
since there is a more general concept of being k-connected.

=item articulation_points

Expand Down Expand Up @@ -1068,7 +1068,14 @@ See L</"Clearing cached results">.
For a directed graph, return true if the directed graph is weakly
connected, false if not.

Weakly connected graph is also known as I<semiconnected> graph.
A weakly connected graph is also known as a I<semiconnected> graph.

Note that there are two mutually incompatible definitions of "weakly
connected". The definition used here is based on connectedness in the
underlying undirected graph, hence this is also sometimes called
"undirected-connected". -- The other definition, proposed by Graham,
Knuth, and Motzkin in 1972, is currently not available within the
Graph module.

See also L</is_strongly_connected>.

Expand Down Expand Up @@ -1467,7 +1474,7 @@ I<connected graphs>, I<biconnected graphs>, and I<strongly
connected graphs>.

B<NOTE>: if the vertices of the original graph are Perl objects,
(in other words, references, so you must be using C<refvertexed>)
(in other words, references, so you must be using C<refvertexed>)
the vertices of the I<connected graph> are NOT by default usable
as Perl objects because they are blessed into a package with
a rather unusable name.
Expand Down Expand Up @@ -2729,7 +2736,7 @@ is possible via the method

=item could_be_isomorphic

$g0->could_be_isomorphic($g1)
$g0->could_be_isomorphic($g1)

=back

Expand Down Expand Up @@ -2760,13 +2767,20 @@ Returns a map of vertices to their Freeman's betweennesses:

C_b(v) = \sum_{s \neq v \neq t \in V} \frac{\sigma_{s,t}(v)}{\sigma_{s,t}}

It is described in:
It is described in

Freeman LC. A set of measures of centrality based on betweenness. 1977.
https://www.scribd.com/document/580201172/A-Set-of-Measures-of-Centrality-Based-on-Betweenness

and in

Freeman, A set of measures of centrality based on betweenness, http://arxiv.org/pdf/cond-mat/0309045
Newman MEJ. A measure of betweenness centrality based on random walks. 2003.
http://arxiv.org/pdf/cond-mat/0309045

and based on the algorithm from:
The implementation is based on the algorithm from:

"A Faster Algorithm for Betweenness Centrality"
Brandes U. A faster algorithm for betweenness centrality. 2000.
https://doi.org/10.1080/0022250X.2001.9990249.

=item clustering_coefficient

Expand Down
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