## Introduction

Welcome to our eighth optional online lecture in the Fall 2015 Introduction to Sociology course at URock! This week, we dive into visualization of the social structure of groups and networks. A node is simply something that can communicate. A tie is simply a communication. An affiliation is the act of belonging. From this simple basis, it is possible to describe a wide variety of social network and group structures. Social network analysis is one of the hottest areas in sociology right now, and this week provides just a tiny peek into it. If you’re interested in learning more, consider taking COM/SOC 375 in the fall — it’s an entire course on nothing but social networks.

## The Structural Basics of Social Networks

A social network describes patterns of relationships between *nodes* (things that can relate to one another) and *ties* (some kind of relation). Watch the video below to find out how simple a social network can be… and yet how many different kinds of structures there are to identify in a network:

These are actually just a few of the varieties of structures that can stem from networks… some other structures have names like “transitive triad,” “clique” and “sociometric star.” But know the structures named in the video above, and you’ll have a good start.

## Three Ways to Draw a Network: Graphs, Lists and Matrices

In the video above, you’ll notice that social networks were always drawn in the form of pictures. Formally speaking, these pictures are called “sociograms” or “network graphs,” and our understanding of these network graphs draws from an entire branch of mathematics called “graph theory.

This isn’t the only way to depict a network. We could take a simpler approach than this. Take a look at the network graph below describing relations between Al, Betty, Cleo, Dan and Enid, and look at the alternatives:

We could just *list* all the ties with a dash between two connected nodes on each line, and in creating a list we would have named all the nodes. The advantage of a list is that it is compact and doesn’t require the drawing of any pictures. The disadvantage should be pretty clear, though: can you see the structure in the list? Not very easily! In contrast, the graph has the advantage of being quickly recognizable; even an elementary school child would be able to look at the picture above tell you that Enid is on the edge of this network.

A third way of depicting the network brings it into a format that can be easily read by a computer for analysis. This is the matrix (a subject of another branch of mathematics, matrix algebra). The kind of matrix that describes connections between people in a social network is an *adjacency matrix*, one in which each person is depicted with one row *and* one column. For every combination of a row and a column, there’s a number in a “cell” that tells you whether a tie exists between the people represented in that row and column. A “1” tells you a tie exists, while a “0” tells you a tie is absent. In the matrix above, for instance, there is a “1” for the matrix cell that describes the relationship between Al and Betty; this means they are tied. In the matrix cell describing the relationship between Betty and Dan, however, there is a “0.” This means there is no tie between them.

The matrix may look a bit complicated to you, but it has its advantages. Consider for a moment how many people you know by sight, who you could get in touch with, and who you’ve seen relatively recently in your life — the average person is acquainted with 290 such people. Network graphs are awfully intuitive when the number of nodes and ties in them are small. But try and interpret this network graph featuring 290 nodes:

Ouch! You really can’t make sense out of that larger network, can you? On the other hand, a matrix can handle hundreds or thousands of nodes or even more. All you need to do is add more columns and rows and you’re all set. Ask a computer to help you count what’s in those cells and you can analyze some pretty interesting real-life network structures.

## Groups Have Structure, Too: the Affiliation Matrix

Groups, the structures described in Chapter 5 of *You May Ask Yourself*, have structure that can be depicted using a matrix, too. It’s just a different kind of matrix: an *affiliation matrix *(to “affiliate” is to belong to a group, to be a member). In an affiliation matrix, each person has its own row and each group has its own column. Every cell of the matrix describes a combination of one row and one columns — one person and one group. If a matrix cell equals “1,” that indicates the person in the row of that cell is a member of the group for the column of that cell. If a matrix cell equals “0,” this means that the person of that row is not a member of the group

Soccer Team | Robotics Club | Student Council | |

Alice | 1 | 1 | 0 |

Ben | 0 | 1 | 1 |

Celia | 1 | 1 | 0 |

Dan | 0 | 0 | 1 |

In the sample affiliation matrix above, Alice is a member of the soccer team and the robotics club, but she is not a member of the student council. The robotics club has Alice, Ben and Celia as members, but Dan is not a member.

You may have noticed two important facts regarding the affiliation matrix and the adjacency matrix. First, as with almost everything else in sociology, we’re discussing *variables*! The variable in an *adjacency *matrix is the answer to the question “is person A tied to person B?” The variable in an *affiliation* matrix is the answer to the question, “is person A a member of group B?” Second, just as important as considering where the ties and memberships are (the “1” values in these matrices) is considering where the ties and memberships are not (the “0” values in these matrices). Who isn’t connected to whom? Who isn’t joining groups? Why? These are valuable questions.

## From Groups to Networks: The Duality of People and Groups

Why would you want to start measuring group structure? Sociologist Ronald Breiger asked this question four decades ago and realized an important way in which groups and networks are connected to one another. The key, Breiger discovered (Breiger 1974), was in the relationship between the adjacency matrix and the affiliation matrix. This video explains the connection and demonstrates in an informal way how it’s possible to move from groups to networks, from mode to mode:

Creating networks of people from membership lists is of vital importance. If you’ve completed the reading by Kieran Healey for this week, you’ll know that the British could have caught a colonial “terrorist” before 1776 if only they had this technique. As Barton Gellman and Ashkan Soltani show in the Washington Post (Gellman and Soltani 2013), the U.S. government today is using exactly this technique to find “fellow travelers” who they consider dangerous.

## Know These Elements of Network Analysis

Remember these elements of network structure from this lecture:

*Node**Tie**Directed Network**Undirected Network**Degree, Indegree, Outdegree**Distance**Cut Point**Density**List**Adjacency Matrix**Affiliation Matrix**The Duality of People and Groups*- 1-mode network
- 2-mode network

Have a question about any of these? Post a comment below and I’ll respond to your question right away.

## References

Breiger, Ronald L. 1974. “The Duality of Persons and Groups.” *Social Forces* 53(2): 181-190.

Gellman, Barton and Ashkan Soltani. 2013. “NSA Tracking Cellphone Locations Worldwide, Snowden Documents Show.” *Washington Post,* December 4.

Healy, Kieran. 2013. “Using Metadata to Find Paul Revere.” *KieranHealy.org*, June 9.