Dynamic Centrality Measures for Financial Contagion New Paradigms for Modeling Dynamic Graphs across Disciplines

Abstract

Abstract: Networks are an ubiquitous form of social organization that have come to punctuate the way in which information can be processed and distributed among large groups. In this report we explore dynamic networks: networks whose properties change over time. In Part 1, we are interested in designing metrics that will help us identify social referents in Massive Open Online Courses – by which we mean students who wield considerable influence in online course forums – who can be targeted by instructors to disseminate an understanding of critical concepts in the course. This can be extended to community detection, whereby we attempt to find groups of students that exhibit similar in-group behavior, but are dissimilar when compared to other groups. In Part 2, we repurpose those metrics to identify systemically risky banks in financial networks – by which we mean banks whose bankruptcy could prompt the subsequent bankruptcies of several other banks, starting a financial contagion. We do this by employing a novel particle simulation framework that maps dynamic networks into Euclidean space, allowing measurements of centrality, social distance, and community strength to be computed geometrically. The networks under study are co-occurrence networks of student participation in MOOC forums, and the cross-holdings network for European banks between 2008 and 2013.