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For inbound links to be effective, it's as quick as it takes for G to index the site they come from and register those links to your site. Effectiveness then measured by the quality of that link.
So most people are seeing the effect of good links pretty much as soon as G has registered their existence and factored them into your ranking score for a given term? Does that sound reasonable?
That said, there are a few ways by which we can ensure (or at least do our best to ensure) that Google is made aware of these "trustworthy" links:
2. Look at the most recent cache date. Was it several days ago? Perhaps you can even time the link placement to go live when the page is due for another caching.
3. I may get some heat for saying this, but Bruce Clay's LinkMaps tool actually serves its purpose pretty well. If you've been using the LinkMaps pages for a while and all the initial spidering has been done, you might find that you've done a fairly good job of showing Google some links that they may or may not have already known about.