This paper investigates the market structure of the insurance business by analyzing the (interlock) linkages among companies created by their directors. We focus on the non-life business since this is a sector relatively closed with respect to the competition with other financial activities; an absence of industry competition cannot thus be compensated by other agents. We apply the graph theory to describe the network and the principal component analysis to summarize information and verify the correlation between direct interlocking and companies' market shares.