Provided by: libbio-perl-perl_1.6.901-2_all

#### NAME

```       Bio::Coordinate::Graph - Finds shortest path between nodes in a graph

```

#### SYNOPSIS

```         # get a hash of hashes representing the graph. E.g.:
my \$hash= {
'1' => {
'2' => 1
},
'2' => {
'4' => 1,
'3' => 1
},
'3' => undef,
'4' => {
'5' => 1
},
'5' => undef
};

# create the object;
my \$graph = Bio::Coordinate::Graph->new(-graph => \$hash);

# find the shortest path between two nodes
my \$a = 1;
my \$b = 6;
my @path = \$graph->shortest_paths(\$a);
print join (", ", @path), "\n";

```

#### DESCRIPTION

```       This class calculates the shortest path between input and output coordinate systems in a
graph that defines the relationships between them. This class is primarely designed to
analyze gene-related coordinate systems. See Bio::Coordinate::GeneMapper.

Note that this module can not be used to manage graphs.

Technically the graph implemented here is known as Directed Acyclic Graph (DAG). DAG is
composed of vertices (nodes) and edges (with optional weights) linking them. Nodes of the
graph are the coordinate systems in gene mapper.

The shortest path is found using the Dijkstra's algorithm. This algorithm is fast and
greedy and requires all weights to be positive. All weights in the gene coordinate system
graph are currently equal (1) making the graph unweighted. That makes the use of
Dijkstra's algorithm an overkill. A simpler and faster breadth-first would be enough.
Luckily the difference for small graphs is not significant and the implementation is
capable of taking weights into account if needed at some later time.

Input format
The graph needs to be primed using a hash of hashes where there is a key for each node.
The second keys are the names of the downstream neighboring nodes and values are the
weights for reaching them. Here is part of the gene coordiante system graph::

\$hash = {
'6' => undef,
'3' => {
'6' => 1
},
'2' => {
'6' => 1,
'4' => 1,
'3' => 1
},
'1' => {
'2' => 1
},
'4' => {
'5' => 1
},
'5' => undef
};

Note that the names need to be positive integers. Root should be '1' and directness of the
graph is taken advantage of to speed calculations by assuming that downsream nodes always
have larger number as name.

An alternative (shorter) way of describing input is to use hash of arrays. See
Bio::Coordinate::Graph::hash_of_arrays.

```

#### FEEDBACK

```   Mailing Lists
User feedback is an integral part of the evolution of this and other Bioperl modules. Send
is much appreciated.

bioperl-l@bioperl.org                  - General discussion
http://bioperl.org/wiki/Mailing_lists  - About the mailing lists

Support
Please direct usage questions or support issues to the mailing list:

bioperl-l@bioperl.org

rather than to the module maintainer directly. Many experienced and reponsive experts will
be able look at the problem and quickly address it. Please include a thorough description
of the problem with code and data examples if at all possible.

Reporting Bugs
report bugs to the Bioperl bug tracking system to help us keep track the bugs and their
resolution.  Bug reports can be submitted via the web:

https://redmine.open-bio.org/projects/bioperl/

```

#### AUTHOR-HeikkiLehvaslaiho

```       Email:  heikki-at-bioperl-dot-org

```

#### APPENDIX

```       The rest of the documentation details each of the object methods. Internal methods are
usually preceded with a _

Graph structure input methods
graph
Title   : graph
Usage   : \$obj->graph(\$my_graph)
Function: Read/write method for the graph structure
Example :
Returns : hash of hashes grah structure
Args    : reference to a hash of hashes

hash_of_arrays
Title   : hash_of_arrays
Usage   : \$obj->hash_of_array(%hasharray)
Function: An alternative method to read in the graph structure.
Hash arrays are easier to type. This method converts
arrays into hashes and assigns equal values "1" to
weights.

Example : Here is an example of simple structure containing a graph.

my \$DAG = {
6  => [],
5  => [],
4  => [5],
3  => [6],
2  => [3, 4, 6],
1  => [2]
};

Returns : hash of hashes graph structure
Args    : reference to a hash of arrays

Methods for determining the shortest path in the graph
shortest_path
Title   : shortest_path
Usage   : \$obj->shortest_path(\$a, \$b);
Function: Method for retrieving the shortest path between nodes.
If the start node remains the same, the method is sometimes
able to use cached results, otherwise it will recalculate
the paths.
Example :
Returns : array of node names, only the start node name if no path
Args    : name of the start node
: name of the end node

dijkstra
Title   : dijkstra
Usage   : \$graph->dijkstra(1);
Function: Implements Dijkstra's algorithm.
Returns or sets a list of mappers. The returned path
description is always directed down from the root.
Called from shortest_path().
Example :
Returns : Reference to a hash of hashes representing a linked list
which contains shortest path down to all nodes from the start
node. E.g.:

\$res = {
'2' => {
'prev' => '1',
'dist' => 1
},
'1' => {
'prev' => undef,
'dist' => 0
},
};

Args    : name of the start node
```