I am adding the next rewrite towards the conf apply for my virtual host:

RewriteEngine On
RewriteCond %{HTTP_HOST} ^example.com
RewriteRule (.*) http://www.example.com/$1 [R=301,L]
.... A bunch of aliases here

The website works fine using the www. but when one enters the domain with no www. the website is going to be rerouted to www.example.com/home/example/public_html - it adds the file path. How do i prevent this?

Here's the aliases:

Alias /index.php /home/cms/public/index.php
Alias /skins/admin /home/cms/public/skins/admin
AliasMatch ^/scripts/(\w+)/admin/(\w+)\.js /home/cms/modules/$1/scripts/admin/$2.js
AliasMatch ^/scripts/(\w+)/(\w+)\.js /home/cms/modules/$1/scripts/$2.js
Alias /scripts /home/cms/public/scripts 
AliasMatch (?i)^/flash/([A-Za-z]*)/([A-Za-z_]*).swf$ /home/cms/public/flash/$1/$2.swf
Alias /css /home/cms/public/css
Alias /thirdparty /home/cms/public/thirdparty
RewriteEngine off
<Directory /home/cms>
    Order allow,deny
    Allow from all
<Location />
    RewriteEngine On
    RewriteCond %{REQUEST_FILENAME} -s [OR]
    RewriteCond %{REQUEST_FILENAME} -l [OR]
    RewriteCond %{REQUEST_FILENAME} -d
    RewriteRule ^.*$ - [NC,L]
    RewriteRule ^.*$ /index.php [NC,L]

Based on documentation, you will have the local path within the regex, prior to the grouping:

RewriteRule ^\/home\/example(.*) http://www.example.com$1 [R=301,L]

Also based on the paperwork:

Around the first RewriteRule [the Pattern] is used towards the (%-decoded) URL-path from the request subsequent designs are put on the creation of the final matched up RewriteRule.

This could suggest you've other RewriteRules just before that certain.