Social Network Analysis (SNA) is a research method used to study social relations among one or more sets of actors, such as family members. SNA allows you to use a systems perspective to study interactions within a group or among groups. There are research journals dedicated to SNA methods. The statistics involved can be simple or quite complex, depending on the approach you take to SNA. Here are some great resources on Social Network Analysis:
Eric Widmer, University of Geneva, studies family networks. This useful article, below, introduces SNA to family scholars.
Widmer E. D., & La Farga L.A. (2000). Family networks: A sociometric method to study relationships in families. Field Methods, 12, 2, 108-128.
Peter Marsden has written many outstanding articles on Social Network Analysis. One useful article is:
Marsden, P. (1990). Network data and measurement. Annual Review of Sociology, 16, 435-463.
David Knoke, has a very popular Social Network Analysis course here at the University of Minnesota. There are terrific resources on his course website.
James Moody, Duke, offers a course on Social Network Analysis. You can refer to his course syllabus and more.
This website, analytictech.com, also has an Introduction to Network Analysis, including handouts arranged by topic.