Social media is considered a democratic space in which people connect and interact with each other regardless of their gender, race, or any other demographic factor. Despite numerous efforts that explore demographic factors in social media, it is still unclear whether social media perpetuates old inequalities from the offline world. In this paper, we attempt to identify gender and race of Twitter users located in U.S. using advanced image processing algorithms from Face++. Then, we investigate how different demographic groups (i.e. male/female, Asian/Black/White) connect with other. We quantify to what extent one group follow and interact with each other and the extent to which these connections and interactions reflect in inequalities in Twitter. Our analysis shows that users identified as White and male tend to attain higher positions in Twitter, in terms of the number of followers and number of times in user's lists. We hope our effort can stimulate the development of new theories of demographic information in the online space.