Preliminaries

This chapter contains technical background for the material addressed throughout the rest of the book. We begin in Section 2.1 with an overview of necessary topics from graph theory, which provides us with much of the language and infrastructure for manipulating and describing networks and network data. We then turn in Section 2.2 to a brief review of fundamental elements from probability and statistical inference, which will provide us with most of the language and principles used here for the modeling and analysis of network data. Finally, in Section 2.3, we discuss, through a series of examples, some of the unique challenges inherent in the statistical analysis of network data. Readers sufficiently familiar with both graph theory and statistical inference may wish to skip this chapter and move directly to Chapter 3, after perhaps a quick detour to glance through the examples of Section 2.3 and the issues raised therein.