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We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long- range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r) ∼ r �δ . Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2 4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ 2 there is no percolation transition as in regular linear chains. Copyright c EPLA, 2011 Complex networks have attracted considerable atten- tion in the last decade (1-12). It has been realized that networks provide a very useful way to describe and better understand the collective behavior of complex systems composed of a large number of interacting entities. There are two network classes of particular interest: Erdos-Renyi (ER) random graphs (13) and Barabasi-Albert (BA) scale- free networks (14). In ER networks, the distribution of the degrees k (number of links) of the nodes is a Poissonian (P (k) ∼ λ k /k!, where λ is the average degree), while in BA scale-free networks, the distribution follows a power law, P (k) ∼ k �γ , with γ typically between two and three. Both classes have interesting topological properties, consider- ably different from those of regular lattices. Both exhibit the "small world" effect meaning that their topological diameter increases slowly, either logarithmically or double logarithmically, with the system size (9,10). When studying the properties of networks it is usually assumed that spatial constraints can be neglected.