Is a natural link profile a ranking signal? No. You don't get better rankings because your link profile looks "more natural" than another website. It's more of a spam signal. If your link profile looks unnatural, you could get penalized. But there's no scale for being more or less natural, there's just natural or unnatural.
A natural link profile has a variety of backlinks. Those links come from a variety of sources. Those links have varied anchor texts. Those links have varied placements on the different pages. Those links are pointing to a variety of your internal pages. The links come from different types of websites.
As far as showing link totals and growth in a graph, Majestic SEO is great, but it's easy to do yourself in Excel. I do it that way because Majestic goes back 4 or 5 years and sometimes I'm more interested in just seeing progress over the last few months.
