Performing efficient decentralized search is a fundamental problem in Peer-to-Peer (P2P) systems. There has been a significant amount of research recently on developing robust self-organizing P2P topologies that support efficient search. In this paper we discuss four structured and unstructured P2P models (CAN, Chord, PRU, and Hypergrid) and three characteristic search algorithms (BFS, k-Random Walk, and GAPS) for unstructured networks. We report on the results of simulations of these networks and provide measurements of search performance, focusing on search in unstructured networks. We find that the proposed models produce small-world networks, and yet none exhibit power-law degree distributions. Our simulations also suggest that random graphs support decentralized search more effectively than the proposed unstructured P2P models. We also find that on these topologies, the basic breadth-first search algorithm and its simple variants have the lowest search cost.