An Index for Measuring Spatial Graph Dispersion in Socio-Economic Networks

Spatial or geographical distance is influential in many socio-economic networks, but its combination with graph theoretical analysis is challenging. In this study, we define a node and network level spatial dispersion index which combines tie strength and spatial distance in a weighted graph to measure average spatial dispersion of socio-economic activities. The index is computed using an average of tie distances weighted with tie strengths. We define weighted vs unweighted, directed vs undirected, and generalized variants of the index. We demonstrate the use of our index to analyse the network of migration flows between provinces of Turkey by (1) comparing the geographic outreach of migration from provinces in different regions, (2) comparing spatial dispersion of migration to different country level spatial networks of flow such as trade, travel, or health services, and (3) testing effects of population and economic development on spatial dispersion of migration. Our results use weighted vs unweighted, and directed vs undirected variants of the index. Since the index is not problem specific, its use not only prove useful in quantifying features of the network in focus but also allows comparison across different networks. Results of this application demonstrate the suitability of the new index in quantifying and comparing the socio-economic activity in geographically dispersed networks and interpreting the differences.