The goal of Google is to return the most relevant and accurate websites for the keywords that you typed in and they use a lot of factors to decide which websites to show and in what order. One of the most important factors is backlinks, that is, links pointing to your website. When the internet first started, webmasters use to link to webpages which they thought were a good resource and Google used that info in their algorithm to return better search results.
Sites which have lots of backlinks from different domains (sources) will eventually triumph in the SERPs. Equipped with that knowledge, SEOers started to manipulate the system by artificially creating those links to the sites they wanted to rank. When Google indexed those backlinks, it naturally increased their prominence in the search engine result pages and with this have come a gaming system where people will try mercilessly to spam the whole web space to get better rankings.
People started buying more and more domains as they are quite cheap and link them to their money making sites. Web hosting is quite cheap if you shop around and most hosting packages will allow you to host unlimited domain names through add-on domains or domain parking. This makes it really easy for someone to get better rankings.
However Google started to crack down on this scheme and a measure was put in place to see where the backlinks were coming from. Shared hosting allows you to host multiple websites but on only 1 IP address; that IP is shared among all the sites which are hosted on the server. You can have on average 500 sites on a shared server. This does not necessary mean that they all belong to one person but in most cases, they belong to maybe 200-300 people who have purchased website hosting with that company. The problem that arises if you have for example, Website B and C linking to Website A, is that Google will give less importance to the links from those websites if they are hosted on the same server (same IP). This is of course a simple demonstration but in the real world, one website may be getting thousands of links from other website on the same IP address.
If that happens, then there will be no real benefits to your rankings from an SEO perspective. Therefore if you really want to benefit from other websites you may own, it is best if you host them on multiple IPs.
Some web hosting providers have realised that many people were looking into diversifying the IPs associated with their domains and therefore have launched what is now called seo hosting. The main feature that differentiates this product from others is that your hosting will include more IPs for you to use on your domains. For example, you might choose an seo hosting with 10 IPs if you had 10 different domains for which you wanted seo benefits when interlinking. An IP address looks something like this : 126.96.36.199 and the third digit represents the Class C block of that IP. Organisations are usually given the same Class C block and that’s how Google can determine if you’re hosting all the websites yourself.
An alternative to seo hosting would be to buy web hosting from different hosts. You’re after different IP addresses, right? So if you get hosting from different companies, you’re bound to get different IP addresses. And this might cost you cheaper than getting 10 IPs on the same hosting. Note that some providers allow you to purchase additional IPs for a monthly cost but that would work out more expensive to be honest.
Conclusion is that if you really must interlink your website for an seo benefit, then you might as well get them linked from different IPs or don’t do it at all. However another problem that you might face is that if all domains are owned by the same person, then Google can eventually use that info to ascertain how many websites are owned by the same individual and despite having different IPs for it, you might not get good rankings.