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	# find the edge. assume it only exists once -> only delete the first.
	# while we're at it, delete the edge from the source vertex...
	my $e = $self->{vertices}->{$from}->{edges_out}->{$to};
	return undef if (!defined($e));
	delete($self->{vertices}->{$from}->{edges_out}->{$to});

	# now search it in the destination vertex' list, delete it there
	# also only delete the first matching one here (though now there
	# shouldn't be any duplicates at all because now we're matching the
	# actual edge, not just its endpoints like above.
	delete($self->{vertices}->{$to}->{edges_in}->{$from});

	# and remove it from the graph's vertex list
	@{$self->{edges}} = grep { $_ != $e } @{$self->{edges}}
}

1;

__END__