Status group membership is important in everyday classrooms and during breaks. Students’ classification may include rejected and controversial individuals (1). In classrooms popular or rejected groups have been shown to be stable over several years. Peer interaction conserves and exaggerates the cluster label (2). Classrooms without outliers indicate a lower risk of malaise (3). Furthermore the problem with marginalized individuals is related to whether individual students become discriminated. The situation with existing discrimination due to status, gender or ethnicity is closely related to segregation. The problem of segregation and discrimination was recently addressed in a report concerning member states of EU (4), which acknowledges segregation on school level. Considerable variation of segregation may occur between districts within a country (5). Gustafsson (6) has recently pointed out the need for investigation of school segregation in Sweden. Thus, it is of great relevance to investigate aspects of segregation and exclusion in classrooms. The hypothesis is that an individual is more segregated the more the members of his/her group interact only with each other. The Spectral Segregation Index (SSI) provides a new measure of segregation and integration among groups of people based on quantitative data on interpersonal relationships. The index, pioneered by Echenique and Fryer (7), has been applied to residential and school segregation among different ethnical groups in the United States (7, 8). Theoretically the index is based on the Perron-Frobenius theorem on eigenvalues and eigenvectors of irreducible non-negative matrices in linear algebra, hence the reference to “spectral’’. Here we propose to use SSI to measure similar parameters among school children. To the best of our knowledge, studies with this method have not been conducted previously in Europe. The special property of the SSI that makes it interesting for our purpose is its capability not only to measure integration/segregation for a group of people, such as a school class, but also to provide measures for individual pupils. This makes it possible to merge the data from the individual level with other kinds of individual data and draw conclusions concerning correlations between levels of integration/segregation and other characteristics of the individuals. The first purpose of the study was to evaluate variations in computed individual and group mean SSI when weights, i.e. strengths of interpersonal relationships, assigned according to the nomination by the peers, are varied. The second purpose was to give examples of the usefulness of SSI from different aspects.

Self reports on attitudes from 1540 students in 78 classes in grade 6 in Göteborg (9) was used. Each student was asked to write the first name (and the first initial of the last name) of the 3 peers he/she preferred to work with in the class room, and preferred to play with during breaks, in the order 1-3. Foreign or Nordic ethnicity was decided from the first name. The data was quantified by assigning numerical weights to the choices, resulting in a, generically non-symmetric, weighted adjacency matrix of inter-personal strength of relationships. The sum of weights given to the 3 choices of a student should always be 1 (7). The mathematical conditions can be met by symmetrizing the adjacency matrix. The highest eigenvalue yields the integration measure for the group and the corresponding eigenvector provides individual indices. The indices are computed using software such as MATLAB™.

When different weights were applied (0.5; 0.34; 0.16) on the 3 choices, individuals with high status emerged clearly. A highly appreciated student during work could have low popularity during breaks. With similar weights (0.34; 0.33; 0.33) more students seemed to gain popularity, and another pattern emerged. Obviously, there is a fair amount of arbitrariness in the assignment of weights. On the other hand, one can argue for a range of quite natural choices. By varying the weights we can investigate the stability of the indices to different choices of weights, and in that way gauge the strength of the subsequent conclusions. Other aspects of usefulness of the method are the possibility to compare gender patterns within different classrooms and patterns of interaction within classrooms with different proportions of “immigrants” and Nordic individuals. Furthermore, segregated clusters and rejected students can be visualized.