Measuring connectedness among financial institutions is central in many aspects of financial economics, including system-wide risk monitoring and identifying systemically risky institutions. In this work, we present a unified framework for measuring connectivity among firms or asset classes from multivariate time series data. The proposed framework relies on regularized estimation of high-dimensional vector autoregressive models (VAR), is flexible enough to incorporate grouping and latent structures among firms, allows parallel implementation for large data sets and enjoys strong statistical guarantees under high-dimensional scaling. We apply our method to analyze connectivity among stock returns of leading financial firms in the U.S. before, during and after the financial crisis of 2007-2008, and demonstrate promising results in detecting important systemic events and systemically risky institutions.