A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, N, as the only parameter, two parameters including N and a second parameter α are included in our formula. The parameter α is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.
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.
To accurately track computer viruses,an overlay network that monitors the activities of viruses is constructed.Identifying and locating nodes infected by virus on network is achieved by a naming system in which a node in the network is mapped to a unique serial number of the hard-drive.By carefully monitoring and recording sensitive communication between local system and remote nodes on the network,and suspicious operations on files that originate from remote nodes and entered via some form of file transfer,activities of viruses in both local and network level are recorded and ready for future analysis.These data can also be used in analysis of the mechanism of a computer virus as well as its spreading mode and pattern.
Li YingCao YiqunQiu BenJiao JianShan XiumingRen Yong
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.
Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.
