I have links to images on my website (fined with lightbox),
when I extend the links with
rel="lightbox nofollow" would this increase the link juice value of the other links? I don't need all of the images indexed, a few of em.
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More PageRank would flow through the links that don't contain the
nofollow link relationship yes.
It is not advisable to
nofollow links for the benefit of manipulating PageRank though (PageRank sculpting) - for content that you do not wish to be indexed or crawled, it should contain the meta
NOINDEX tag (pages) or be disallowed in the
robots.txt (files and directories).
As pointed out in the comments, by nofollowing internal links on your website, this no longer causes more PageRank to flow via the followable links.
This illustration from Moz demonstrates how PageRank flows pretty well:-
And to cite a snippet from this article:-
So what happens when you have a page with “ten PageRank points” and ten outgoing links, and five of those links are nofollowed? Let’s leave aside the decay factor to focus on the core part of the question. Originally, the five links without nofollow would have flowed two points of PageRank each (in essence, the nofollowed links didn’t count toward the denominator when dividing PageRank by the outdegree of the page). More than a year ago, Google changed how the PageRank flows so that the five links without nofollow would flow one point of PageRank each.
Thanks to @Binarysurf for the clarification of this.
nofollow will not improve your SERP's at all, neither will share more pagerank to other links inside a page. So, you better don't do it, it will hurt your site.
It's not recommended to use
nofollow on internal links because it drops (Matt Cutts said "evaporates") pagerank. Links
nofollowed are taken into account when calculating pagerank distribution between all links inside a page, then, their pagerank part is dropped.
Why blocking your images? It's better if all of your content (pages, images, video, etc.) are indexed, every single item might be another door for letting visitors get into your site.