The Venetian republic was one of the most successful trans-modern states, surviving for a millennium through innovation, commercial cunning, exploitation of colonies and legal stability. Part of the success might be due to its government structure, a republic ruled by a doge chosen among a relatively limited set of Venetian patrician families. In this paper we analyze the structure of the social network they formed through marriage, and how government was monopolized by a relatively small set of families, the ones that became patrician first.