[R] how to convert careers to social network description

[Philipp Chapkovski]

There is a dataframe in R that looks that
Person --- Organization --- Year In --- Year Out
   P1                X               2001        2005
   P2                X               2002        2006

What is the most quick way to convert it to the table of the
connections between two people with a 'strength' equal the number of
years they worked together?
In this example the result should be something like:
Person 1 --- Person 2 --- Strength
     P1             P2              4

It seems to me that should be some quick and compact way to do this
conversion but I don't know how. Thank you for any hints!

Philipp