Balance-theoretic models and incomplete signed digraphs

Ž . The initial structural models based on balance theory structural balance and clusterability dealt with Ž . incomplete signed digraphs. However, newer models ranked clusters, transitivity, hierarchical M-cliques apply only to zero-one matrices representing either unsigned digraphs or complete signed digraphs. Since empirical networks of affective relations are signed but seldom complete — actors may have neutral feelings towards alters or affections may be unknown to the researcher — the latter models must be redefined if affective relations are to be analysed. It was found that each balance-theoretic model is characterised by a particular type of semicycle or path. Counts of the types of semicycles and paths suffice to identify the models. This approach is more general than triadic analysis because it handles complete as well as incomplete signed digraphs. q 1999 Elsevier Science B.V. All rights reserved. Ž . Classification code: Social network analysis 0665 ; Methodology and research technology; Research methŽ . odsrtools 0104