Predicting the Evolution of a Constrained Network: A Beta Regression Model

Social network analysis allows to map and measure relationships and flows (links) between people, groups, computers, URLs, or other connected knowledge entities (nodes). In this context, a relevant issue is the treatment of constrained scale-free networks such as the network of student transfers between degree courses offered by an University, that are strongly influenced by a number of institutional decisions. In the analysis of such a system, special attention has to be paid to identify current or future “critical points”, that is nodes characterized by a high number of outcoming or incoming links, on which to act in order to optimize the network. To predict the evolution of a constrained system over time in dependence of constraint modifications, a beta regression model is proposed, that fits links represented by quantities varying between 0 and 1. The algorithm was successfully applied to the network of student transfers within the University of Bologna: the link was defined by the out-transfer rate of the degree course (computed as the ratio of the number of out-transfers to the number of students enrolled) and the critical points of the system were defined by the courses characterized by a high out-transfer rate.