Janet,
The use of social media tools expand and enhance career services abilities to serve students such as the examples you provide on how you'd specifically like to use LinkedIn. However, this is not an example of a "community partnership" as explained in the course. The use of social media tools are similar to using any other tool at one's disposal to achieve goals (i.e. the internet, a phone, a fax machine, mobile apps, etc.). Beyond your desire to use social media tools, was your intention to express some sort of actual partnership between the company, LinkedIn, and your institution? Can you please explain in the event others have misunderstood?
Additionally, playing devil's advocate, I would ask why limit one's self to a single tool like LinkedIn? Why not use multiple tools with different intent to accomplish goals? Certainly, there are many advantages to using Facebook as a means to mine for data, strategically engage with graduates and students, build affinity among the student/graduate population, build online communities via pages, profiles or groups, etc. You may be interested in reviewing CS104 - Developing a Social Media Strategy for Career Services.
Robert Starks Jr.