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Social Network Analysis (in 10 minutes) Nick Crossley

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A set of methods for analysing patterns of relationships. Visualising them in graphs. Visualising them in graphs. Defining and measuring their properties. Defining and measuring their properties. Representing and manipulating them in matrices. Representing and manipulating them in matrices.

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Often involves: Multidimensional scaling. Multidimensional scaling. Correspondence analysis. Correspondence analysis. Matrix algebra. Matrix algebra. Cluster analysis. Cluster analysis. Conventional stats (regression etc.) Conventional stats (regression etc.) Multilevel modelling Multilevel modelling And certainly should involve qualitative methods too And certainly should involve qualitative methods too

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But best known for: Sociograms (a.k.a. graphs, network maps, social network diagrams). Sociograms (a.k.a. graphs, network maps, social network diagrams). Graph theory applications/measures. Graph theory applications/measures.

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A graph: relationships between actors involved in the early UK punk movement

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Social relations in a private health club:

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More social relations in a private health club:

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Some Network Properties

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DENSITY The actual number of connections in a network expressed as a proportion of the potential number. The actual number of connections in a network expressed as a proportion of the potential number. Given as a figure between 0 and 1. Given as a figure between 0 and 1.

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Diameter The shortest path between the two most distant vertices (vertex = node) in a network. The shortest path between the two most distant vertices (vertex = node) in a network. Path and distance both measured by degree (i.e. links in the chain). Path and distance both measured by degree (i.e. links in the chain). = path/distance of 3 = path/distance of 3

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Centrality (of vertices/nodes) Number of connections (degree centrality). Number of connections (degree centrality). Cumulative shortest distance to every other vertex in the graph (closeness centrality). Cumulative shortest distance to every other vertex in the graph (closeness centrality). Extent to which lies in the path connecting all other vertices (betweenness centrality). Extent to which lies in the path connecting all other vertices (betweenness centrality).

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The focus is on form Definition of vertices is up to researcher. Definition of vertices is up to researcher. Likewise definition of relations. Likewise definition of relations. But of course they must be meaningful and relevant in the context of the project. But of course they must be meaningful and relevant in the context of the project.

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Blockmodelling A method for reducing large data sets. A method for reducing large data sets. Theoretically tied to role analysis and a specific conception of social structure (but perhaps problematically so). Theoretically tied to role analysis and a specific conception of social structure (but perhaps problematically so). Vertices assigned to blocks on the basis of structural equivalence (or regular equivalence). Vertices assigned to blocks on the basis of structural equivalence (or regular equivalence). Relations between blocks (via their vertices) analysed. Relations between blocks (via their vertices) analysed.

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Why bother? Operationalises (some versions of) the concept of social structure. Operationalises (some versions of) the concept of social structure. Network positions enable/constrain actors. Network positions enable/constrain actors. Network figurations enable/constrain actors and have effects. Network figurations enable/constrain actors and have effects. Exploring diffusion. Exploring diffusion. Exploring structural vulnerability. Exploring structural vulnerability.

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How is this going to make us 100K Applications of Graph Theory.

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