You should submit your resume to popular job sites and directly to companies. Skip the internships as you are way past that especially with a Masters degree (would have been ok if you were just starting college, but your have moved past that part now).
Since you have a Masters degree you are worth more out of the box now then before you started college. Since you had summer jobs that counts as work experience but it is concerning, you should be able to get a job as a network administrator if the work you did earning your degree was more practical than theory which it should have been. If not you might be in trouble if you do not know the basics to at least intermediate of setting up a network by yourself. If the latter is the case then you have some serious work to do. By now you should have earned a few certifications (CCNA, MCSE, etc.) to help supplement your academic course work, if not I would recommend getting these out of the way so when you do apply for jobs the employers can take you more seriously as you would have a standardized knowledge base but no long term work experience.
Something else you should also have is a home test rack setup if you had a degree of any kind in networking, which would be the same for someone that took computer science, engineering, software development, etc. all students that normally excelled and were serious about their work had something at home physically or virtually to hone their skills. If this is the case with you then you should have some serious fun at interviews when it comes to the whiteboard questions as you have been through the network setups thousands of times by now and they should be very easy for you by now since you should have mastered it by now.
I would also recommend applying for jobs as big companies like Amazon, Facebook, HP, etc. along with government contractors in your area. As some of the government contractors have the funds to bring you on and train you up in your weak areas all while paying you a very nice salary.
Also no need to take time off, you can work on learning new things when you get home from work