The purpose of this study is to suggest reading education plan by exploring the characteristics of peer-relationship networks of elementary school students, and grasping the effects of those characteristics on the reading competencies. Social network analysis method was used, and centrality analysis, QAP correlation and QAP multiple regression analyses were conducted to examine the relationship between peers and reading competencies. The findings show that the help relationship rather than peer characteristics and friend relationship was related to reading competencies. However, since the friend relationship has an effect on the help relationship, it is also found that the relationship between the friend and the help relationship network should be considered in order to improve the reading competencies. This network analysis results are meaningful in reading education plan in the sense that they suggest a useful guideline for the formation of members ranging from individuals, small groups, to a whole class, and for periodical activities considering situation and learning purposes such as before, during, and after reading activities.