Geodetic convex boundary curvatures of the communities in stock market networks

We analyze the daily returns of stock market indices of NASDAQ and S&P 500 over the period of 2004-2015. We build network models by using a threshold method that captures strong relations amongst the agents. We also subdivide the whole time scale into 20 parts to capture structural changes in networks throughout the global economic crisis of 2008. To determine the dynamics of the structural changes, we use the mimetic discretization of the curvatures on boundaries of communities. We observe different geometric behavior of the boundary throughout the economic crisis. Our findings suggest that the mimetic discretization of boundary curvature is an efficient tool to capture granular structural changes in financial networks.