Keywords: stochastic block models social network community detection
I adapt and apply two recent advances in probability theory in stochastic block models (SBM) to construct a robust model to dynamically represent complex, nonlinear interactions among various features of social networks of corporate board members. SBMs are popular mathematical models of graphs with clusters, which also has come under the term "community detection," where communities are generally understood to be subsets of nodes (or directors on boards) that are more densely interconnected among each other than with the rest of the network. I construct a dynamic SBM for director networks and their evolution over a 20-year period by incorporating information about the quality of board’s external networks, internal cohesiveness, composition in terms of directors’ skill sets and background. As a proxy measure for the quality of external networks, I adapt bi-partite SBMs (bi-SBM) to derive a formulation of the market for corporate directors. Using bi-SBM, I model how the connections between directors on one side and firms on the other evolve dynamically to derive different communities of directors and firms corresponding to different levels of quality over time. As a measure for internal cohesiveness, I will use the size, number and type of communities detected in each board using the dynamic and bi-SBMs. The resulting graph data structure is used in constructing a GBM-based predictive model for company performance based on the S&P 1500 director and performance data from 1996 through 2015. A Python software package that implements the dynamic bi-SBM for analyzing director networks and composition will be released in August of this year.