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 ...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.展开更多
The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite siz...The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.展开更多
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 com...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.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 60672142, 60772053 and 90304005)
文摘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.
基金Project supported by the National Nature Science Foundation of China （Grant Nos 90204004 and 90304005）.
文摘The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.
基金supported by the National Natural Science Foundation of China(Grant Nos 70801066,60674048,60772053 and 60672142)the National Basic Research Program of China(Grant Nos 2007CB307100 and 2007CB307105)
文摘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.
