STANDARDIZING THE SEGMENTATION INDEX S₃

Abstract

The segmentation index S ₃ of Baerveldt and Snijders (1994) is used in the research of social cohesion. However, as is often the case with network level measures, the index is sensitive to network size and density. Therefore, networks of different size or density are not easily comparable. Of course, this seriously limits the research using this index. In this article we propose a standardization of the segmentation index that solves this problem. The standardization uses the expected value and the maximum value of the index, within certain network types, the so-called network families. We show how these values can be calculated. Furthermore, we present a figure that can be used to derive the expected values and a table for easy determination of the maximum values for all network families existing of 4 to 20 members. This allows the calculation of the standardized index for all networks within these families.

Acknowledgments

The authors are grateful to Arnold Meijsters an Ilona Kok for their help in the calculations.

Notes

¹The S₃-measure for segmentation only can handle undirected and unvalued relations between nodes (Baerveldt and Snijders 1994). Therefore, we assume that relations are symmetrical, and that they have no value attached to them. Of course, directed and valued relations can be transformed to undirected and unvalued relations by making the relations symmetrical and by dichotomization of the values. It is evident that this will lead to loss of information.

²In formula:

³The Monte Carlo study was done on a multiprocessor high velocity computer (an SGI Onyx3400 computer, with 12 processors each at 500 MHz). If there were less than M networks in a family W_n,s, no sample was drawn but instead all networks in the family were considered and exact values of E(S₃) and S(S₃) were obtained.

⁴Note that in the literature, sometimes the restriction is used that maximal complete subgraphs are only called cliques if the number of nodes in the subgraph is at least 3. In this article also two-node maximal complete subgraphs are called cliques.