The real deal with link relevance

Im Seo'ing for a local carpet cleaning business and am having a hard time finding niche related links. Ive decided to build a pr0 link network to provide unique niche related content. My question is : When building tier 1,2,3 links to my network, how relevant do my links need to be to carpet cleaning. As I said there arent that many links for that niche. I want to build some links with PR and am not really sure what kind of links to build for this new network. Can I build irrelevant higher PR links to tier 1,2,3 and just rely on my tier 1 blog network for relevant content? And if so what higher PR irrelevant links should I focus on?

I think relevancy should be considered in a scale. Any level of relevancy is good but the deeper the relevancy the better for example:

www / carpetcleaners< most relevant
www / homeimprovement/carpetcleaningtechniques <Highly Relevant
www / carpetcleaners.wordpress/carpetcleaningtechniques <Highly Relevant
www / articlebase/how-to-clean-carpets < relevant
www /ezinearticles/home-improvement <slightly relevant

etc. The higher relevant the link the better, but as long as the content is relevant, there is some relevancy.

Wait, wait, wait...what are you talking about? Local carpet cleaning SEO? Private networks for local carpet cleaning? PR0? Tier 1,2,3?
Dude, are you doing this for yourself or the client? What are you trying to get with that network?
Did you even do a proper KW research, how many competitors etc..?

I built the site on WordPress and optimized all on page and built pretty much all relevant contextual links. It took a year but I have a achieved position one page one for my keywords. I'm just lookin to solidify my rankings long term.

Relevancy of backlinks isn't important. I rank my sites adn clients sites all day utilizing private networks all from "general" niches..

Be cautious of anyone that tells you otherwise