Longitudinal Networks

Networks representing relations that change over time are defined as longitudinal networks; in the social sciences, these relations may correspond to economic transactions or administrative linkages, friendship or family connections, mental and health conditions, communication threads, and associative linkages between organizations and nations.

The interest in the study of longitudinal data dates back to early network analysis, but the problems in elaborating statistical techniques and models have long been an obstacle to research advancement. The problem of autocorrelation of results is one of the specific problems that statistical analysis has to deal with; moreover, the collection of good quality relational data over significant time intervals can be difficult due to sampling differences and reliability of measurements. The evolution of statistical methods and the availability of more detailed information on social exchanges and communication encouraged researchers to elaborate new algorithms and programs suitable for dynamic and longitudinal data. Visualization approaches, in particular, are allowing researchers to investigate time-related changes in the structure and composition of a network and to [Page 508]compare networks of social relations that refer to different stages of an ongoing social process, such as influence or communication.

On the theoretical side, the explanation of change in networks' structure and contents has been approached with strategies that frequently integrate different statistical procedures. More recently, adopted statistical models have highlighted the function of structural elements and selection models separating choice-driven from structural-driven connections. The first types of models consider time as one of the agents of change, implicating possibilities for specific forms of connections (e.g., evolution from dyadic to triadic forms, or from simple linkage to reciprocity links). According to this view, the evolution of a network structure is dependent on the possibilities that are present in the previous stage (the mathematical reference is a Markov chain), such as in the case of preferential attachment phenomena. The second types of models interpret time as the setting of changes at the individual level: the pace of creation and dissolution of network connections (expressed by log-linear functions) is related to individuals' choices and activated by social selection processes that happen in specific time intervals. Both these types of models have been empirically tested, giving satisfactory results; the type of data, however, still influences measurements and computational efficacy.