Examples of social graph in the following topics:
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- Social network analysts use two kinds of tools from mathematics to represent information about patterns of ties among social actors: graphs and matrices.
- On this page, we we will learn enough about graphs to understand how to represent social network data.
- On the next page, we will look at matrix representations of social relations.
- There is a lot more to these topics than we will cover here; mathematics has whole sub-fields devoted to "graph theory" and to "matrix algebra. " Social scientists have borrowed just a few things that they find helpful for describing and analyzing patterns of social relations.
- A word of warning: there is a lot of specialized terminology here that you do need to learn. its worth the effort, because we can represent some important ideas about social structure in quite simple ways, once the basics have been mastered.
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- There are three main reasons for using "formal" methods in representing social network data:
- Matrices and graphs are compact and systematic: They summarize and present a lot of information quickly and easily; and they force us to be systematic and complete in describing patterns of social relations.
- Matrices and graphs allow us to apply computers to analyzing data: This is helpful because doing systematic analysis of social network data can be extremely tedious if the number of actors or number of types of relationships among the actors is large.
- Matrices and graphs have rules and conventions: Sometimes these are just rules and conventions that help us communicate clearly.
- So, we need to learn the basics of representing social network data using matrices and graphs.
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- Social actors are often connected by more than one kind of relationship.
- The friendship graph (figure 3.2) showed a single relation (that happened to be binary and directed).
- Figure 3.4 combines information from two relations into a "multiplex" graph.There are, potentially, different kinds of multiplex graphs.
- We graphed a tie if there was either a friendship or spousal relation.
- But, we could have graphed a tie only if there were both a friendship and spousal tie (what would such a graph look like?
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- Now we need to introduce some terminology to describe different kinds of graphs.
- Figure 3.2 is an example of a binary (as opposed to a signed or ordinal or valued) and directed (as opposed to a co-occurrence or co-presence or bonded-tie) graph.
- Figure 3.3 is an example of a "co-occurrence" or "co-presence" or "bonded-tie" graph that is binary and undirected (or simple).
- The social relations being described here are also simplex (in figures 3.2 and 3.3).
- Figure 3.4 is an example of one method of representing multiplex relational data with a single graph.
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- As we saw in chapter 3, a graph representing the information about the relations among nodes can be an very efficient way of describing a social structure.
- A good drawing of a graph can immediately suggest some of the most important features of overall network structure.
- "neighborhood"), we can get a sense of the structural constraints and opportunities that an actor faces; we may be better able to understand the role that an actor plays in a social structure.
- There is no single "right way" to represent network data with graphs.
- Different ways of drawing pictures of network data can emphasize (or obscure) different features of the social structure.
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- Sociograms, or graphs of networks can be represented in matrix form, and mathematical operations can then be performed to summarize the information in the graph.
- Vector operations, blocking and partitioning, and matrix mathematics (inverses, transposes, addition, subtraction, multiplication and Boolean multiplication), are mathematical operations that are sometimes helpful to let us see certain things about the patterns of ties in social networks.
- Social network data are often multiplex (i.e. there are multiple kinds of ties among the actors).
- Once a pattern of social relations or ties among a set of actors has been represented in a formal way (graphs or matrices), we can define some important ideas about social structure in quite precise ways using mathematics for the definitions.
- In the remainder of the book, we will look at how social network analysts have formally translated some of the core concepts that social scientists use to describe social structures.
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- How can multi-plex relations be represented in graphs?
- Did any studies present graphs?
- If they did, what kinds of graphs were they (that is, what is the technical description of the kind of graph or matrix).
- Pick one article and show what a graph of its data would look like.
- What kinds of relations among them might tell us something about the social structures in this population?
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- In this chapter, we will look at a single directed binary network that describes the flow of information among 10 formal organizations concerned with social welfare issues in one mid-western U.S. city (Knoke and Burke).
- For small networks, it is often useful to examine graphs.
- Figure 7.1 shows the di-graph (directed graph) for the Knoke information exchange data:
- A careful look at the graph can be very useful in getting an intuitive grasp of the important features of a social network.
- To get more precise, and to use computers to apply algorithms to calculate mathematical measures of graph properties, it is necessary to work with the adjacency matrix instead of the graph.
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- It is very useful to describe many social structures as being composed of "directed" ties (which can be binary, signed, ordered, or valued).
- Indeed, most social processes involve sequences of directed actions.
- This is what we used in the graphs above, where individuals (egos) were directing choices toward others (alters).
- In a directed graph, Bob could choose Ted, and Ted choose Bob.
- But, this represents a different meaning from a graph that shows Bob and Ted connected by a single line segment without arrow heads.
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- This view of social structure focuses attention on how solidarity and connection of large social structures can be built up out of small and tight components: a sort of "bottom up" approach.
- Divisions of actors into groups and sub-structures can be a very important aspect of social structure.
- Weaker parts in the "social fabric" also create opportunities for brokerage and less constrained action.
- How separate are the sub-graphs?
- How large are the connected sub-graphs?