Your question is about the data representation of the network topology. The CPAN Graph::Base module defines methods for representing networks efficiently. Given one of your @ip_addrs arrays,

use Graph;

my $G = Graph->new(); # Create Graph object with listed verteces

# Obtain a route in @ip_addrs, then:
add_chain $G, @ip_addrs;

# lather, rinse, and repeat

sub add_chain {
    my $g = shift;
    # add_edge produces any vertices not already present
    $g->add_edge($_[$_-1],$_[$_]) for 1..scalar(@_)-1;
}
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There are many advantages to this. Graph takes care of nasties like cyclic graphs, which would give you trouble in a hand-rolled representation. It has methods like neighbors($vertex), successors($vertex), predecessors($vertex), and many more ('man Graph::Base'). Edges can be weighted by, say, bandwidth to provide support for network traffic analysis.

Hope this helps.

Update: Graph::Base is under the hood of the Graph module. I cited Graph::Base rather than Graph because cpan search on 'Graph' turns up lots of irrelevancies. Here's a link to the tarball, or (with CPAN.pm):
$ perl -MCPAN -e 'shell'
cpan> install Graph
Re: Masem's response, mr_linux wants to scan a 192.168.x/23 network, about 2⁹ IP's. That net may be sparse enough for a simple homegrown representation, but I like the painlessness and power of the Graph module.

After Compline,
Zaxo