Status centrality is a centrality measure inspired by Katz's status index for sociometric analysis (Katz 1953). It assigns larger scores to vertices whose positions in the
graph make them more prominent under the chosen status model. It is used for ranking
actors in sociometric data when status can be inherited through chains of relationships
rather than only through direct ties. In the Wolfram
Language convention, an unnormalized status vector 
satisfies
 |
where 
is the adjacency matrix, 
is the vector of vertex in-degrees, and 
is a graph-determined attenuation factor. This makes status
centrality a Katz-type recursive prestige score with a fixed in-degree baseline.
Isolated vertices are assigned status centrality 0.
Status centrality is implemented in the Wolfram Language as StatusCentrality[g], and precomputed values for named graphs can be requested using GraphData[graph, "StatusCentralities"].
