We've heard of LSI and we know Google sees websites and pages to some degree in terms of themes and relevance. In your view or proven experience do outgoing links affect the Googlebot's interpretation of the site? e.g. If I link out to authority sites on Widgets will my site gain weight in the theme of Widgets? ...or even if my site is about Widgets and I sell links that point out to an Adult site, will I get penalized in some way?
I have no experience with this, but logic would say that no, your site would not gain authority for the search term widgets. I think Google looks at the keywords on the site providing the outgoing link to determine if it is relevant to the target site. If you link to sites that have been banned by Google, you will be penalized, but that is different from what your question is. I don't know about the links to adult sites, but have links to them might result in you not showing up in safe search.
yes, it actually affects the theme of the site...We must build more IBL rather OBL.. IBL is better than OBL...
I've done quite a bit of testing on this, and no there wasn't any SERP shift from out linking to authority sites in the niche or in unrelated niches. Back in around 02 there was a myth linking to Google would improve rank but was found to be false also.
I quote from Google's own Webmaster Guidelines: In particular, avoid links to web spammers or "bad neighborhoods" on the web, as your own ranking may be affected adversely by those links. http://www.google.com/support/webmasters/bin/answer.py?hl=en&answer=35769 So basically this means outgoing links could be counted *against* you. And it makes sense to the concept of LSI that Google algorithms also look at what your pages are pointing at, to determine the theme.
yes, it effects your serp. google is also suggesting you to use less than 100 outgoing backlinks per page.