Peer-to-peer （P2P） networks aggregate enormous storage and processing resources while mini- mizing entry and scaling costs. Gnutella-like P2P networks are complex heterogeneous networks, in which the underlying oveday topology has a power-law node degree distribution. While scale-free networks have great robustness against random failures, they are vulnerable to deliberate attacks where highly connected nodes are eliminated. Since high degree nodes play an important role in maintaining the connectivity, this paper presents an algorithm based on random walks to locate high degree nodes in P2P networks. Simula- tions demonstrate that the algorithm performs well in various scenarios and that heterogeneous P2P net- works are very sensitive to deliberate attacks.
In this paper we will give the statistical characteristics and general principles of an optimal structure of the Internet, which is a scale-free network. Since the purpose of the Internet is to allow fast and easy communication, the average path length is used to measure the performance of the network, and the number of edges of the network is used as a metric of its; cost. Based on this, the goal of this Internet optimization problem is to obtain the highest performance with the lowest cost. A multi goal optimization problem is proposed to model this problem. By using two empirical formulas of （k） and （l）, we are able to find the statistical characteristics of the optimal structure. There is a critical power law exponent ac for the Internet with power law degree distribution, at which the Internet can obtain a relatively good performance with a low cost. We find that this ac is approximately 2.1.
