This article is one of the first approaches to the distribution of leadership in school organizations in Chile. This perspective tries to overcome traditional views by understanding this factor as a function that is distributed in the organization and therefore, can be exercised, not only in a traditional way by the Principal, but by several people which allows to expand their possibilities. It consists in a sample of 51 vulnerable primary schools, from several districts, which in consecutive periods managed to stand out in the SIMCE (Standardized Test of Learning in Chile), among its similar ones. The methodology used is also new in our context, using the ''Social Network Analysis" (ARS), which allows us to collect the real influence relationships that take place in the organization. The results are presented in selected cases, to gather the influencing relationships in the subjects of Management and Pedagogical Management.