2.1 Social Network Analysis: From Relationships to Graphs
Social network analysis is an influential, and now increasingly widespread, methodological approach for analyzing the social world. Traditionally, sociologists have studied relationships using a variety of observational strategies, both qualitative, such as ethnography and interviews, and statistical, such as those based on the social survey. However, beginning in earnest in the 1950s, sociologists began to make concerted use of mathematical techniques from a branch of pure mathematics called graph theory and a branch of applied mathematics called matrix algebra to develop scientific models of social relationships and to come up with measures connecting key concepts from social theory, such as roles, prominence, and prestige, to tangible empirical evidence. Social Network Analysis (SNA) is the use of graph-theoretic and matrix algebraic techniques to study social structure and social relationships.
Figure 0.6: The first picture of a social network, then called a ‘sociogram’ was drawn by Jacob Moreno in 1934. It consisted of the relationships between 19 boys (triangles) and 18 girls (circles) in a 5th grade classroom
This is likely not your first sociology course; but even if it is, relationships are relatively intuitive for people. They are all around us: you and your parents, you and your siblings, your siblings and your parents, you and your classmates, your classmates to each other. Affiliation, communication, friendship, hatred: these are the content of social relationships. Two people either have a relationship of some kind, or they do not. Essentially, a relationship is a connection between at least two social actors.
For example, you are likely enrolled in a social network’s class if you are reading this, and have people you know such as your friends and people you’ve taken prior classes with, but also people you’ve never seen before. It might be obvious that you have a relationship with those people that you know, but do you have a relationship with those you do not know?
The answer is maybe. It depends on how you define the term social relationship. If you were asked who your friends are, you would tell me that some of your classmates are your friends, and the rest of your classmates are not your friends. If you were asked which of these people in your classroom are your classmates however, everyone would be your classmate, except for your professor or teaching assistants. You share a particular type of relationship with these other people, your classmates, even if you’ve never met them. The word “classmate” even implies a relationship type, one with a different social meaning than “friend.” When analyzing a social network, it is important to first understand what type of social relationship you are analyzing, as it relates directly to what type of conclusions or generalizations you can make about the social world.
Once you have a type of social relationship you would like to examine, the next step is to bound the context. If you want to map out all the social relationships in the world, well that’s impossible. Imagine how difficult it would be to map out all the people at your school who are friends with one another. That might be feasible if you have only 1,000 undergraduates, but at a school of 30,000, it would be a nightmare. That is in part why it is so important to bound the social context. The other is to exclude relationships that are not meaningful for your study. Bounding, or to draw boundaries, is to have a rule about what will or will not be included in the study (Laumann, Marsden, and Prensky 1989Laumann, Edward O, Peter V Marsden, and David Prensky. 1989. “The Boundary Specification Problem in Network Analysis.” In Research Methods in Social Network Analysis, edited by Linton C. Freeman, Douglas R. White, and Antone Kimball Romney, 61–79. New Brunswick: Transaction Publishers.).
Figure 0.7: The Zachary karate club network study was one of the first data collection probjects in the history of SNA. The data are famous for showing how networks could be used to find groups based on the relations between actors.
For example, if you are interested in who is friends with who in your social networks class, you have bound your study to look at only people who are in your social networks class. One of the most famous social network studies was performed by the anthropologist Wayne W. Zachary (see Figure 0.7) at a college karate club in the early 1970s (Zachary 1977Zachary, Wayne W. 1977. “An Information Flow Model for Conflict and Fission in Small Groups.” Journal of Anthropological Research 33 (4): 452–73.). Thus, the 34 members of the karate club and the outside teacher were the actors included in the study because they were the people who were involved in the day to day operations of the karate club at the time data were collected.
With a type of social relationship in some bounded context, you can begin to map the social world as a graph. In its most basic form, a graph is essentially a picture of the relationships between different types of social actors. This picture becomes incredibly powerful when we begin to use mathematical concepts to understand how actors relate to each other (mostly what this book is concerned with) or upon what social principles the network may have been formed (addressed in an extent in this book, but much more powerful statistical techniques such as exponential random graph models that are not presented here in detail).
2.1 Social Network Analysis: From Relationships to Graphs
Social network analysis is an influential, and now increasingly widespread, methodological approach for analyzing the social world. Traditionally, sociologists have studied relationships using a variety of observational strategies, both qualitative, such as ethnography and interviews, and statistical, such as those based on the social survey. However, beginning in earnest in the 1950s, sociologists began to make concerted use of mathematical techniques from a branch of pure mathematics called graph theory and a branch of applied mathematics called matrix algebra to develop scientific models of social relationships and to come up with measures connecting key concepts from social theory, such as roles, prominence, and prestige, to tangible empirical evidence. Social Network Analysis (SNA) is the use of graph-theoretic and matrix algebraic techniques to study social structure and social relationships.
This is likely not your first sociology course; but even if it is, relationships are relatively intuitive for people. They are all around us: you and your parents, you and your siblings, your siblings and your parents, you and your classmates, your classmates to each other. Affiliation, communication, friendship, hatred: these are the content of social relationships. Two people either have a relationship of some kind, or they do not. Essentially, a relationship is a connection between at least two social actors.
For example, you are likely enrolled in a social network’s class if you are reading this, and have people you know such as your friends and people you’ve taken prior classes with, but also people you’ve never seen before. It might be obvious that you have a relationship with those people that you know, but do you have a relationship with those you do not know?
The answer is maybe. It depends on how you define the term social relationship. If you were asked who your friends are, you would tell me that some of your classmates are your friends, and the rest of your classmates are not your friends. If you were asked which of these people in your classroom are your classmates however, everyone would be your classmate, except for your professor or teaching assistants. You share a particular type of relationship with these other people, your classmates, even if you’ve never met them. The word “classmate” even implies a relationship type, one with a different social meaning than “friend.” When analyzing a social network, it is important to first understand what type of social relationship you are analyzing, as it relates directly to what type of conclusions or generalizations you can make about the social world.
Once you have a type of social relationship you would like to examine, the next step is to bound the context. If you want to map out all the social relationships in the world, well that’s impossible. Imagine how difficult it would be to map out all the people at your school who are friends with one another. That might be feasible if you have only 1,000 undergraduates, but at a school of 30,000, it would be a nightmare. That is in part why it is so important to bound the social context. The other is to exclude relationships that are not meaningful for your study. Bounding, or to draw boundaries, is to have a rule about what will or will not be included in the study (Laumann, Marsden, and Prensky 1989Laumann, Edward O, Peter V Marsden, and David Prensky. 1989. “The Boundary Specification Problem in Network Analysis.” In Research Methods in Social Network Analysis, edited by Linton C. Freeman, Douglas R. White, and Antone Kimball Romney, 61–79. New Brunswick: Transaction Publishers.).
For example, if you are interested in who is friends with who in your social networks class, you have bound your study to look at only people who are in your social networks class. One of the most famous social network studies was performed by the anthropologist Wayne W. Zachary (see Figure 0.7) at a college karate club in the early 1970s (Zachary 1977Zachary, Wayne W. 1977. “An Information Flow Model for Conflict and Fission in Small Groups.” Journal of Anthropological Research 33 (4): 452–73.). Thus, the 34 members of the karate club and the outside teacher were the actors included in the study because they were the people who were involved in the day to day operations of the karate club at the time data were collected.
With a type of social relationship in some bounded context, you can begin to map the social world as a graph. In its most basic form, a graph is essentially a picture of the relationships between different types of social actors. This picture becomes incredibly powerful when we begin to use mathematical concepts to understand how actors relate to each other (mostly what this book is concerned with) or upon what social principles the network may have been formed (addressed in an extent in this book, but much more powerful statistical techniques such as exponential random graph models that are not presented here in detail).