This paper addresses the way in which the level of trust in cooperative relations depends on network structures. The study is an elaboration of models developed in earlier papers using iterated games [Weesie, J., Buskens, V., Raub, W., 1998. The management of trust relations via institutional and structural embeddedness. Journal of Mathematical Sociology (in press); Buskens, V., 1995. Social Networks and the Effect of Reputation on Cooperation. ISCORE Paper No. 42, Utrecht University]. We distinguish individual and group network measures. Applying a combination of approximation methods to the game-theoretic solution to the model, we derive hypotheses on the effects of density, outdegree centrality, and centralization on the level of trust a truster can have in a trustee. We conclude that higher density and outdegree induce more trust. Centralization increases trust if it is 'well organized,' i.e., actors who can place more trust are central in the network. Furthermore, we discuss theoretical evidence that the relative importance of density compared to outdegree increases if the trust problem at the dyadic level is large. Finally, we show that, in many situations, a few simple network measures explain most of the effects of the network structure as a whole. (C) 1998 Elsevier Science B.V. All rights reserved.