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.

实证网络的时间演化研究通常聚焦于其演化后期阶段，此时持久连接已然趋于稳定。关于网络早期发展历程的实证数据较为稀缺，却又是深入理解现实社交网络拓扑结构演化机制的必要支撑。研究一群刚进入大学、此前彼此几乎没有或仅有少量联系的新生，为探究社交网络的连接模式与社区结构的形成与早期演化提供了独特契机。在为期九周的大学物理入门课程中，研究人员要求一年级物理专业学生列出前一周与其讨论物理解题思路的交流对象。我们基于这些学生的自我报告构建了随时间变化的学生交互网络。我们对该类网络展开分析，以阐明不同学生属性在网络早期形成过程中可能产生的影响。每周连接数量的变化情况显示，尽管约半数连接会在周际发生更新，但随着课程推进，学生们也会重新建立起越来越多的交互连接。借助Infomap社区检测算法（Infomap community detection algorithm），我们发现该类网络呈现出社区结构，并利用性别、课程期末成绩等非网络结构属性对社区形成阶段的社群特征进行刻画。具体而言，我们提出了一种隔离度测度（segregation measure），并证明学生社群的形成依据为性别与预先编排的教学班（学生在此开展物理解题与实验室实验活动），而非课程期末成绩。连续周度社区的冲积图（Alluvial diagrams）显示，尽管学生在学习初期的组间流动较为随机，但在课程后期会趋于稳定。综合来看，这些分析结果表明，学生交互网络会快速趋于稳定，且学生们的协作关系建立在身边可接触的对象与可观测的个人特征之上。