The scale-fee networks, having connectivity distribution P (k) ∼ k −α (where k is the site connectivity), is very resilient to random failures but fragile to intentional attack. The purpose of this paper is to find the network design guideline which can make the robustness of the network to both random failures and intentional attack maximum while keeping the average connectivity < k > per node constant. We find that when < k >= 3 the robustness of the scale-free networks reach its maximum value if the minimal connectivity m = 1 , but when < k > is larger than four, the networks will become more robust to random failures and targeted attacks as the minimal connectivity m gets larger.Keywords: Scale-free network; optimal programme; power-law distribution; random failure.competition. To the exist growing scale-free network, we can not convert its topology into the theoretical optimization directly disobeying its evolutionary principle. But we can improve the network robustness. Firstly, we must know the optimal guideline to maximum the scale-free network robustness.The p total c characterizes the robustness of the scale-free network to random failures and intentional attacks simultaneously. In this paper we analyze the scale-free network robustness to both random failures and intentional attacks simultaneously and find that the minimum degree of the network is very important to the scale-free network robustness with a constant < k >. To an exist growing scale-free network, if the network average degree per node is around three, we should keep its minimum degree around one to improve the network robustness. But if the network average connectivity is larger than four, we should add its minimum degree to improve its robustness to both attacks, which mean that the relationship between the minimum connectivity nodes would become very important for the network robustness.
In this paper, we studied the research areas of Chinese natural science basic research from a point view of complex network. Two research areas are considered to be connected if they appear in one fund proposal. The explicit network of such connections using data from 1999 to 2004 is constructed. The analysis of the real data shows that the degree distribution of the research areas network (RAN) may be better fitted by the exponential distribution. It displays small world effect in which randomly chosen pairs of research areas are typically separated by only a short path of intermediate research areas. The average distance of RAN decreases with time, while the average clustering coefficient increases with time, which indicates that the scientific study would like to be integrated together in terms of the studied areas. The relationship between the clustering coefficient C(k) and the degree k indicates that there is no hierarchical organization in RAN.
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