The influence of directors has been one of the most engaging topics recently, but surprisingly little research has been done to quantitatively evaluate the influence and power of directors. We analyze the structure of the US corporate governance network for the 11-year period 1996-2006 based on director data from the Investor Responsibility Research Center director database, and we develop a centrality measure named the influence factor to estimate the influence of directors quantitatively. The US corporate governance network is a network of directors with nodes representing directors and links between two directors representing their service on common company boards. We assume that information flows in the network through information-sharing processes among linked directors. The influence factor assigned to a director is based on the level of information that a director obtains from the entire network. We find that, contrary to commonly accepted belief that directors of large companies, measured by market capitalization, are the most powerful, in some instances, the directors who are influential do not necessarily serve on boards of large companies. By applying our influence factor method to identify the influential people contained in the lists created by popular magazines such as Fortune, Networking World, and Treasury and Risk Management, we find that the influence factor method is consistently either the best or one of the two best methods in identifying powerful people compared to other general centrality measures that are used to denote the significance of a node in complex network theory.