Previous research indicates that race, ethnicity, and gender influence legislative behavior in important ways. The bulk of this research, however, focuses on the way these characteristics shape an individual legislator's behavior, making it less clear how they account for relationships between legislators. We study the cosponsorship process in order to understand the race and gender based dynamics underlying the relational component of representation. Using a temporal exponential random graph model, we examine the U.S. House cosponsorship network from 1981 through 2004. We find that Black and Latino members of Congress are at a comparative disadvantage as a result of race-based assortative mixing in the cosponsorship process, yet this disadvantage is mitigated by the electoral pressures that all members face. Members representing districts with significant racial and ethnic minority populations are more likely to support their minority colleagues. We also find that women members do not appear to face a similar disadvantage as a result of their minority status. We argue that these race and gender dynamics in the cosponsorship network are the result of both the inherent tendency towards intra-group homophily in social networks and the electoral connection, which is manifested here as members supporting minority colleagues to broaden their own electoral base of support among minority constituencies.