Applications of eigenvector centrality to small social networks

• This article investigates conceptual and methodological questions that may arise in applying eigenvector centrality to small social networks such as school classes. The focus on small networks brings out surprising and subtle properties related to the interpretation of the measure. We investigate examples where the weighted adjacency matrix of the underlying social network quantifies inter-individual preferences of whom to work with or play with. We show that mathematical operations such as transposition and symmetrization of the weighted adjacency matrix enhances the power of the measure. It is demonstrated that it is not sufficient to work with the original weight matrix. By working with a symmetrized or a semi-symmetrized or a transposed weight matrix different characteristics of the social interaction are revealed. The method chosen depends on the purpose of the investigation. Identifying isolated or popular individuals in the network are also facilitated using these operations.

Keyword

eigenvector

centrality

small

social

networks

peer relations

integration

Teacher Education and Education Work

Lärarutbildning och pedagogisk yrkesverksamhet

Publication and Content Type

vet (subject category)

ovr (subject category)