This paper explores efficient search algorithms in power-law networks, which are characterized by a few highly connected nodes (hubs) and many low-degree nodes. The authors introduce local search strategies that leverage these high-degree nodes and scale sub-linearly with the graph size. These strategies are particularly useful in peer-to-peer networks like Gnutella, where geographic location is not a reliable indicator of target nodes. The paper presents analytical results and simulations to demonstrate the effectiveness of these algorithms, showing that they can significantly reduce search costs compared to random walks. The authors also compare the performance of their algorithms with those on Poisson random graphs, highlighting the advantages of power-law networks in terms of search efficiency. Finally, the paper discusses the implications of these findings for large social networks and the Internet backbone, suggesting that the power-law structure of these networks naturally facilitates information distribution and search.This paper explores efficient search algorithms in power-law networks, which are characterized by a few highly connected nodes (hubs) and many low-degree nodes. The authors introduce local search strategies that leverage these high-degree nodes and scale sub-linearly with the graph size. These strategies are particularly useful in peer-to-peer networks like Gnutella, where geographic location is not a reliable indicator of target nodes. The paper presents analytical results and simulations to demonstrate the effectiveness of these algorithms, showing that they can significantly reduce search costs compared to random walks. The authors also compare the performance of their algorithms with those on Poisson random graphs, highlighting the advantages of power-law networks in terms of search efficiency. Finally, the paper discusses the implications of these findings for large social networks and the Internet backbone, suggesting that the power-law structure of these networks naturally facilitates information distribution and search.