Though the graphical model was introduced in 1980, most of the research and application of the methodology in this field has been done by Europeans. The U.S. has lagged somewhat behind; only in recent years has the graphical model appeared in some of the American textbooks on categorical data, and even then the coverage is limited. The purpose of this work is to provide an initial source of reading for someone interested in the topic. This publication distinguishs itself from any other book by including the multigraph representation of LLMs, a natural and very effective extension of the graphical model approach. The book's coverage would extend from the LLM, already covered by Knoke and Burke's SAGE publication, "Log-Linear Models," through the development and application of the multigraph representation in one coherent, comprehensive treatment.