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We define geometric self-structuring in a large-scale networked system as the ability of the participating nodes to collaboratively impose a geometric structure to the network. Self-structuring is hard to achieve when no global positioning information about the network is available. Yet this is an useful capability in networked autonomous systems such as sensor networks. In this paper, we present the design and the evaluation of a fully decentralized geometric self-structuring approach. This approach heavily relies on the ability of each node to estimate its position in the network. The contribution of the paper is twofold: (i) a simple and fully decentralized virtual coordinated system (VINCOS) is proposed, relying only on local connectivity information and per-neighbor communication; (ii) a network geometric self-structuring approach (NetGeoS) is presented that enables a large set of nodes to configure themselves in arbitrary geometric structures. The evaluation shows that the approach is both efficient and accurate while achieving the geometric structuring. [ABSTRACT FROM AUTHOR]