In many countries, the representation of women on corporate boards of directors has become a topic of intense political debate. Social networking plays a crucial role in the appointment to a board so that an informed debate requires knowing where women are located in the network of directors. One way to quantify the network is by studying the links created by serving on the same board and by joint appointments on multiple boards. We analyse a network of $\approx 320\,000$ board members of $36\,000$ companies traded on stock exchanges all over the world, focusing specifically on the position of women in the network. Women only have $\approx 9-13\%$ of all seats, but they are not marginalised. Applying metrics from social network analysis, we find that their influence is close to that of men. We do not find evidence to support previous claims that women play the role of "queen bees" that exclude other women from similar positions.