Welcome to the documentation and analysis portal for Distinction Centrality (\(\beta_i\)).
This project implements and analyzes a social network metric theoretically inspired by Pierre Bourdieu’s theory of agonistic competition in social fields. It models the trade-off between status (influence/eigenvector centrality) and constraint (average status of neighbors in the node-deleted subgraph).
Mathematical Formulation
The distinction centrality (\(\beta_i\)) of a node \(i\) is defined as:
\[\beta_i = \alpha s_i - \kappa_i\]
where: - \(s_i\) is the status of node \(i\). - \(\kappa_i\) is the constraint (average status of neighbors in the node-deleted subgraph). - \(\alpha\) is a scalar adjustment factor defined as \(\alpha = \frac{\bar{\mathbf{\kappa}}}{\bar{\mathbf{s}}}\).
Explore the tabs above to learn more about the implementation and see real-world examples using historical social network datasets.