The old thinking is that the grad department of a school doesn’t want to accept undergrads from the same school. It’s been changing; the world is much smaller now.
A few months back, I had a conversation on this subject with two friends of mine, one being a world-famous EE professor at UCB, the other currently a researcher at UCB (I’m not sure of his title, but he’s not teaching and way beyond post-doc), both having volunteered in ad com at UCB CoE for a number of years. While admitting to the so-called “common wisdom,” they told me that there were many much more important factors in grad admission than “being undergrad from the same school.” They also told me that they had never seen a candidate being rejected for the reason of being undergrad at UCB.
PhD students these days have a lot of opportunities to work with grad departments of other schools. Also, what’s wrong with having an undergrad degree from the best undergrad school and also having a grad degree from the best grad school? The best undergrad school and the best grad school happen to be the same, so what!
I personally know at least two undergrads at UCB currently doing PhD at UCB, one EE, the other CS. They were also admitted to other grad schools, but chose UCB partly because UCB was simply the best in the fields they wanted to study.
Case in point: Prof. Tsu-Jae King Liu received the B.S., M.S. and Ph.D. degrees in Electrical Engineering from Stanford University (you should know Prof. Liu if you’re going to UCB).