Time development in the early history of social networks: link stabilization, group dynamics, and segregation

Studies of the time development of empirical networks usually investigate late stages where lasting connections have already stabilized. Empirical data on early network history are rare but needed for a better understanding of how social network topology develops in real life. Studying students who are beginning their studies at a university with no or few prior connections to each other offers a unique opportunity to investigate the formation and early development of link patterns and community structure in social networks. During a nine week introductory physics course, first year physics students were asked to identify those with whom they communicated about problem solving in physics during the preceding week. We use these students' self reports to produce time dependent student interaction networks. We investigate these networks to elucidate possible effects of different student attributes in early network formation. Changes in the weekly number of links show that while roughly half of all links change from week to week, students also reestablish a growing number of links as they progress through their first weeks of study. Using the Infomap community detection algorithm, we show that the networks exhibit community structure, and we use non-network student attributes, such as gender and end-of-course grade to characterize communities during their formation. Specifically, we develop a segregation measure and show that students structure themselves according to gender and pre-organized sections (in which students engage in problem solving and laboratory work), but not according to end-of-coure grade. Alluvial diagrams of consecutive weeks' communities show that while student movement between groups are erratic in the beginnning of their studies, they stabilize somewhat towards the end of the course. Taken together, the analyses imply that student interaction networks stabilize quickly and that students establish collaborations based on who is immediately available to them and on observable personal characteristics.