When I was first looking at Norwegian, and later Danish, a few years ago, someone recommended "Naiv Super" by Erlend Loe as a good book for starting readers, as it is written in a literally naive style, with relatively simple sentences. I neve got around to reading any Scandinavian version of it at that time, but I did read it in English and German, and read another of his books in German.
I thought I'd look at what Amazon.co.uk had in Norwegian, and found this interesting version of "Naiv Super" aimed specifically at English speaking learners:
http://www.amazon.co.uk/Naiv-Super-Nels ... 74&sr=1-33
Naiv. Super.: Volume 1 (Nelsbok) (Norwegian) Paperback – 4 Sep 2015
Naiv. Super. is a story, naively yet poignantly imagined, about a young Norwegian man who suddenly finds himself in a crisis. To discover what's going on--and to rediscover himself--he drops out of his studies at the university, sells most of his belongings, and moves into his brother's unoccupied apartment. Through contemplation and play, he sorts through life's meanings, tries to gain perspective on the world, revisits his lost childhood, and becomes obsessed with the concept of time. After several weeks, he joins his brother for a vacation in New York City, where, with his brother's help, he finds how best to live life. The side-column glossary and Norwegian-to-English dictionary compiled exclusively for this book make this edition of Loe's original text ideal for language learners and lovers of Norway and Norwegian culture.
Judging by the pages one can read online, it looks a bit like some graded readers I have seen, with explanations on each page for some words on each page, but by no means all. This is quite an interesting alternative to parallel texts, as it means you are pretty much forced to work out some of the words/expressions from context, and you may have to look some things up, but at least you are probably not having to look up every word. So you are given help, but you aren't handed everything on a plate, so to speak. Psychologically, this seems a good approach to me, and it helped me a lot when I was using graded readers in Welsh. This is not actually a graded reader, since it is a full version of the book (I assume), but as already mentioned, the original is written in a simple style which should be accessible to the beginner who has some grasp of the basics already, and mainly wants to increase vocabulary.
...
Completely unrelated, I happened upon this page of links to various Norwegian resources, which I pass on to anyone who might be interested:
http://norsknett.typepad.com/my_weblog/ ... egian.html
...
If there are any other learners (or like me, re-starters) of Norwegian on the forum, I would be interested in hearing from you. Maybe we can pool ideas, especially, suggestions of books/audiobooks to read/listen to.