The conformation space of a 20-residue antiparallel $��$-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 pathway