How can I find the connected components of a graph in Perl? - linux

Question

I have the following collection of nodes and edges. What I want to do is to find all the distinct graph from it.
my %connections=(36=>[31],10=>[3,4],31=>[30,22],30=>[20],22=>[20,8],20=>[1],8=>[5],5=>[2],2=>[1,20], 3=>[7]);
In this example it will yield:
my %all_graph = {
graph1 => {36=>[31],31=>[30,22],30=>[20],22=>[20,8],20=>[1],8=>[5],5=>[2],2=>[1,20]}.
graph2 => {10=>[3,4], 3=>[7]}
};
Is there any existing algorithms that does that?

Answer 1

Use the Graph module:
#!/usr/bin/perl
use strict; use warnings;
use Graph;
my %connections = (
36 => [ 31 ],
10 => [ 3, 4],
31 => [ 30, 22],
30 => [ 20 ],
22 => [ 20, 8],
20 => [ 1 ],
8 => [ 5 ],
5 => [ 2 ],
2 => [ 1, 20 ],
3 => [ 7 ]
);
my $g = Graph->new( undirected => 1 );
for my $src ( keys %connections ) {
for my $tgt ( #{ $connections{$src} } ) {
$g->add_edge($src, $tgt);
}
}
my #subgraphs = $g->connected_components;
my #allgraphs;
for my $subgraph ( #subgraphs ) {
push #allgraphs, {};
for my $node ( #$subgraph ) {
if ( exists $connections{ $node } ) {
$allgraphs[-1]{$node} = [ #{ $connections{$node} } ];
}
}
}
use YAML; print Dump \#allgraphs;
Output:
[sinan#archardy SO]$ ./g
---
- 2:
- 1
- 20
20:
- 1
22:
- 20
- 8
30:
- 20
31:
- 30
- 22
36:
- 31
5:
- 2
8:
- 5
- 10:
- 3
- 4
3:
- 7

Answer 2

To find the connected components of an undirected graph you just do a BFS or DFS (Breadth/Depth first search).
Here some sample BFS code
my %connections=(36=>[31],10=>[3,4],31=>[30,22],30=>[20],22=>[20,8]
,20=>[1],8=>[5],5=>[2],2=>[1,20], 3=>[7]);
my $full_connections = {}; # Build a REAL graph with full 2-way edge lists
foreach my $node (keys %connections) {
foreach my $node2 (#{ $connections{$node} }) {
print "$node, $node2\n";
$full_connections->{$node}->{$node2} = 1;
$full_connections->{$node2}->{$node} = 1;
}
}
my %all_graph = ();
my $current_graph = 0;
my %visited = ();
my #to_visit = ();
foreach my $node (keys %$full_connections) {
next if exists $visited{$node};
# start the next segment
$current_graph++;
#to_visit=($node);
while (#to_visit) {
$node_to_visit = shift #to_visit;
#next if $visited{$node_to_visit};
$visited{$node_to_visit} = $current_graph;
push #to_visit, grep { !exists $visited{$_} }
keys %{ $full_connections->{$node_to_visit} };
}
}
# Now reconstruct %all_graph from %visited - left as exercise for the reader
print Data::Dumper->Dump([\%visited]);

Answer 3

I'd suggest the following algorithm:
1.) Move all nodes into a working set N.
2.) Starting with an arbitrary node perform a graph search (depth-first or breadth-first). Add all visited nodes and edges to the first subgraph, remove visited nodes from N
3.) If N is non-empty, select the next starting node and go to step 2.) for the next subgraph.