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Y. Huang, J. Neidhardt:
"From Networks to Space: Constructing Metric Spaces for Social Interactions";
Vortrag: Empirical Investigation of Social Space II, Bonn, Germany; 12.10.2015 - 14.10.2015.

Bourdieu´s field theory provides a relational framework to bridge objective ties and subjective relations in complex social systems. The important concepts, field and habitus, provide essential building blocks for constructing social space. Although field theory has been tested in various social settings, many of them only focused on a particular domain of social structures and avoid the nature of multi-dimension and overlapping social structures. On the other hand, the advancement of online social communities such as Facebook and online games has generated enormous network data reflecting the underlying social interactions. This provides opportunities and challenges to study intertwisted social groups and illustrate the structure of a much larger social space.
Despite of his advocacy of relational thinking, Bourdieu argued against social network analysis based on individual exchange and interactions and preferred correspondence analysis, which concentrates on objective relations, e.g. differential levels of capitals. Nooy (2003) compared correspondence analysis and social network analysis and argued that objective relations and individual interactions have a mutual influence and both should be used for identifying people´s positions in the social space. The recent progress of Exponential Random Graph Models (ERGM/p*) provides advanced techniques to extract underlying formation mechanisms (part of habitus) from the structures of observed individual interactions. However, due to the computational complexity, this method is only feasible for small and homogenous networks.
In this paper, we propose hyperbolic embedding as a nexus to integrate field theory and social network analysis. As type of geometric data analysis, hyperbolic embedding supports more flexible dimensional reduction and eliminates the 2D restriction of correspondence analysis; meanwhile, as Krioukov et al. (2010) have shown, hyperbolic embedding also characterizes the link probability in exponential random graphs. Therefore, we obtain a unified metric space (through hyperbolic embedding) that represents an ensemble of capitals and interactions and provides positions of individuals and their distances in social space. To demonstrate the method, we use large networks from online communities such as Second Life to construct a metric space of hundreds of thousands people and illustrate the shapes of local structures.

Bourdieu´s field theory provides a relational framework to bridge objective ties and subjective relations in complex social systems. The important concepts, field and habitus, provide essential building blocks for constructing social space. Although field theory has been tested in various social settings, many of them only focused on a particular domain of social structures and avoid the nature of multi-dimension and overlapping social structures. On the other hand, the advancement of online social communities such as Facebook and online games has generated enormous network data reflecting the underlying social interactions. This provides opportunities and challenges to study intertwisted social groups and illustrate the structure of a much larger social space.
Despite of his advocacy of relational thinking, Bourdieu argued against social network analysis based on individual exchange and interactions and preferred correspondence analysis, which concentrates on objective relations, e.g. differential levels of capitals. Nooy (2003) compared correspondence analysis and social network analysis and argued that objective relations and individual interactions have a mutual influence and both should be used for identifying people´s positions in the social space. The recent progress of Exponential Random Graph Models (ERGM/p*) provides advanced techniques to extract underlying formation mechanisms (part of habitus) from the structures of observed individual interactions. However, due to the computational complexity, this method is only feasible for small and homogenous networks.
In this paper, we propose hyperbolic embedding as a nexus to integrate field theory and social network analysis. As type of geometric data analysis, hyperbolic embedding supports more flexible dimensional reduction and eliminates the 2D restriction of correspondence analysis; meanwhile, as Krioukov et al. (2010) have shown, hyperbolic embedding also characterizes the link probability in exponential random graphs. Therefore, we obtain a unified metric space (through hyperbolic embedding) that represents an ensemble of capitals and interactions and provides positions of individuals and their distances in social space. To demonstrate the method, we use large networks from online communities such as Second Life to construct a metric space of hundreds of thousands people and illustrate the shapes of local structures.