How do you get links that are both authoritative and relevant
The answer lies precisely in the definition of the two terms. The authority of a page is mainly defined by its backlinks. So if you get a backlink from a page that has many strong and authoritarian backlinks, you've got a link with authority.
Relevance is assessed on several parameters:
Contents
URL
Title Tag
Website theme / topic
So why is BT not relevant to the webshop selling bicycles?
Because BT's content is not about bicycles. Page URL, Title Tag and General Theme are not about bikes.
So a link from BT will be an authoritarian link, but not particularly relevant.
But!
What if BT wrote a comprehensive article about bicycles where these were in play:
Title Tag: Here are the nominations for the best bikes in 2017
URL: BT dot dk / de-beste-cykler-2017
So, all SEO people would agree that a link from this page is incredibly relevant and authoritarian. One might even think about giving it a score of 8/10.
8/10 is quite nice, but how do you get up to 10/10?