- 1 Introduction
- 2 Graphs
- 2.1 Social Network Analysis: From Relationships to Graphs
- 2.2 The Building Blocks of Graphs: Edges and Nodes
- 2.3 Symmetric Relations and Undirected Graphs
- 2.4 Asymmetric Relations and Directed Graphs
- 2.5 Anti-Symmetric Ties and Tree Graphs
- 2.6 Order and Size
- 2.7 Average Degree
- 2.8 Degree Distributions
- 2.9 Density
- 2.10 Ego-Centric Networks
- 2.11 Weighted Ties as a Measure of Strength
- 2.12 Di-Graphs
- 2.13 Collecting Network Data
- 2.14 Practice Problems

- 3 Matrices
- 4 Centrality and Composition
- 5 Subgraphs
- 6 Where Do Networks Come From?
- 7 Social Capital: Network Structure and Social Outcomes
- 8 Whole Network
- 9 Diffusion

While we’ve so far examined the principles behind building graphs and matrices to represent network structure, we have yet to touch on how looking at smaller clusters of associations in the network can inform our understanding of the social world. This chapter thus explores how we can think of social activity occuring at the **subgraph** level and not just within the network as a single whole. Our examination of subgraphs starts by presenting some fundamentals from graph theory about we can think about connectivity within networks. Second, we present ideas about how network analysts think about how to identify groups out of relational data. While groups are an intuitive part of how we think about the social world, actually defining groups is an incredibly difficult problem (Moody). Finally, we present algorithms commonly used to break apart larger networks into constituent groups.