# NAME

Graph::AdjacencyMatrix - create and query the adjacency matrix of graph G

# SYNOPSIS

``````    use Graph::AdjacencyMatrix;
use Graph::Directed; # or Undirected

my \$g  = Graph::Directed->new;
\$g->add_...(); # build \$g

my \$am = Graph::AdjacencyMatrix->new(\$g);
\$am->is_adjacent(\$u, \$v)

my \$am = Graph::AdjacencyMatrix->new(\$g, distance_matrix => 1);
\$am->distance(\$u, \$v)

my \$am = Graph::AdjacencyMatrix->new(\$g, attribute_name => 'length');
\$am->distance(\$u, \$v)

my \$am = Graph::AdjacencyMatrix->new(\$g, ...);
my @V  = \$am->vertices();

\$g = Graph->new(multiedged => 1);
\$g->add_...(); # build \$g
\$am = Graph::AdjacencyMatrix->new(\$g, distance_matrix => 1);
\$am->distance(\$u, \$v) # returns hash-ref of ID => distance``````

# DESCRIPTION

You can use `Graph::AdjacencyMatrix` to compute the adjacency matrix and optionally also the distance matrix of a graph, and after that query the adjacencyness between vertices by using the `is_adjacent()` method, or query the distance between vertices by using the `distance()` method.

By default the edge attribute used for distance is `w`, but you can change that in new(), see below.

If you modify the graph after creating the adjacency matrix of it, the adjacency matrix and the distance matrix may become invalid.

# Methods

## Class Methods

new(\$g)

Construct the adjacency matrix of the graph \$g.

new(\$g, options)

Construct the adjacency matrix of the graph \$g with options as a hash. The known options are

distance_matrix => boolean

By default only the adjacency matrix is computed. To compute also the distance matrix, use the attribute `distance_matrix` with a true value to the new() constructor.

attribute_name => attribute_name

By default the edge attribute used for distance is `w`. You can change that by giving another attribute name with the `attribute_name` attribute to new() constructor. Using this attribute also implicitly causes the distance matrix to be computed.

## Object Methods

is_adjacent(\$u, \$v)

Return true if the vertex \$v is adjacent to vertex \$u, or false if not.

distance(\$u, \$v)

Return the distance between the vertices \$u and \$v, or `undef` if the vertices are not adjacent.

If the underlying graph is multiedged, returns hash-ref of ID mapped to distance. If a given edge ID does not have the attribute defined, it will not be represented. If no edge IDs have the attribute, `undef` will be returned.

adjacency_matrix

Return the adjacency matrix itself (a list of bitvector scalars).

vertices

Return the list of vertices (useful for indexing the adjacency matrix).

# ALGORITHM

The algorithm used to create the matrix is two nested loops, which is O(V**2) in time, and the returned matrices are O(V**2) in space.

# AUTHOR AND COPYRIGHT

Jarkko Hietaniemi jhi@iki.fi

# LICENSE

This module is licensed under the same terms as Perl itself.