Enrolling the cultural capital of underrepresented communities in PK-12 technology and curriculum design has been a primary strategy for broadening the participation of students of color in U.S. computer science (CS) fields. This article examines two ways that African-American cultural capital and computing can be bridged in CS education. The first is "community representation," using cultural capital to highlight students' social identities and networks through computational thinking. The second, "computational integration," locates computation in cultural capital itself. I survey two risks--the appearance of shallow computing and the reproduction of assimilationist logics--that may arise when constructing one bridge without the other. To avoid these risks, I introduce the concept of "computational communities" by exploring areas in CS education that employ both strategies. This concept is then grounded in qualitative data from an after school program that connected CS to African-American cosmetology.