A Brief History of Statistical Models for Network Analysis and Open Challenges

Networks are ubiquitous in science. They have also become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active ?social science network community? and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature coming out of statistical physics and computer science. In particular, the growth of the World Wide Web and the emergence of online ?networking communities? such as Facebook, Google+, MySpace, LinkedIn, and Twitter, and a host of more specialized professional network communities have intensified interest in the study of networks and network data. This article reviews some of these developments, introduces some relevant statistical models for static network settings, and briefly points to open challenges.