Aggregating multiple groups in SQL - mysql

Question

I have an application that needs to query a MySQL database and retrieve a list of users that may be sharing an IP address, and I am having some trouble turning my the concept of what I want to do with my query in my head into a functional query.
The situation is that I have a table which contains known ip information for users. Each time the user logs in, it creates a timestamped entry containing their user id and the ip address they logged into.
Initially, I used the following query to return rows representing IP addresses that were shared:
select ip, GROUP_CONCAT(DISTINCT account ORDER BY timestamp SEPARATOR ' ')
from known_ips
group by ip having count(1) > 1
However, many users have dynamic IP addresses so this list contains many duplicate entries (one for each IP address they share with others, obviously).
What I would like to do is have each row returned be a unique group of users that have shared any ip address with one another at any point.
For example, if Bob and Jane had shared IP address 192.168.0.1 and Bob and Fred had shared IP address 192.168.0.2, I would want the row to return 'Bob Fred Jane' (the program is taking the results of this query and doing some operations with it, and essentially needs a list of accounts on which to take action).
What I can't figure out on my own is how to do this aggregation (or whether it is even possible). I initially tried to have the original query as CTE (using with clause) and then trying to group on that, however I reached a stumbling block in that I couldn't figure out how to logically carry out the operation "compare string-delimited list of users in group 1 to see if any exist in group 2", and I figure doing that sort of string comparison is not what SQL is all about anyway (and I can do it in the program rather than the SQL besides).
Does anyone know of any technique whereby I can represent the logic of what I am trying to achieve here in MySQL? Or, should I accept the solution I already reached and then do the aggregation in the client application?
Edit:
In response to the request to a sample of data and output, here is a contrived example of the data:
Account IP Timestamp
Bob 192.168.0.1 2014-02-12 08:00
Bob 192.168.0.1 2014-02-12 09:30
Bob 192.168.0.2 2014-02-12 10:00
Mary 192.168.0.1 2014-03-12 07:00
Bob 192.168.0.2 2014-03-12 08:00
Jim 192.168.0.4 2014-03-12 08:30
Ted 192.168.0.2 2014-03-12 09:00
Jim 192.168.0.5 2014-04-12 08:30
Bob 192.168.0.3 2014-04-12 09:30
Andy 192.168.0.6 2014-04-12 10:30
Paul 192.168.0.6 2014-04-12 11:30
From this sample data, I would expect exactly two rows returned:
Bob Mary Ted
Andy Paul
I am ambivalent about the ordering of accounts in the list, despite my use of ORDER BY timestamp earlier.