The conformation space of a 20-residue antiparallel β-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Conformations are nodes of the network, and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without projections into arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state ensemble, and provides a basis for understanding the heterogeneity of the transition state and denaturated state ensemble as well as the existence of multiple pathways.Keywords: complex networks, protein folding, energy landscape, transition state, denaturated state ensemble, multiple pathwaysProteins are complex macromolecules with many degrees of freedom. To fulfill their function they have to fold to a unique three-dimensional structure (native state). Protein folding is a complex process governed by noncovalent interactions involving the entire molecule. Spontaneous folding in a time range of microseconds to seconds 1 can be reconciled with the large amount of conformers by using energy landscape analysis 2,3,4 . The main difficulty of this analysis is that the free-energy has to be projected on arbitrarily chosen reaction coordinates (or order parameters). In many cases a simplified representation of the free-energy landscape is obtained where important informations on the non-native conformation ensemble and the folding transition state ensemble are hidden. Moreover, the possible transitions between free-energy minima cannot be displayed in such projections which hinder the study of pathways and folding intermediates. The characterization of the free-energy minima and the connectivity among them, i.e., possible transitions between minima, for peptides and proteins is still an unresolved problem.In the last five years many complex systems, like the World-Wide Web, metabolic pathways, and protein structures have been modeled as networks 5,6,7 . Intriguingly, common topological properties have emerged from their organization 8 . A description of the potential energy landscape without the use of any projection has been given in terms of networks for a Lennard-Jones cluster of atoms 9 .Here, we introduce complex network analysis 8 to study the conformation space and folding of beta3s, a designed 20-residue sequence whose solution conformation has been investigated by NMR spectroscopy 10 . The NMR data indicate that beta3s in aqueous solution forms a monomeric (up to more than 1mM concentration) triplestranded antiparallel β-sheet (Fig. ...