Cross Networking Empirical Research And Statistical Laws

This thesis mainly reports on some systems empirical, numerical simulation and model-analytic investigation of cross-network. First, we define the cross-network:there are two networks, if they have the common nodes, we call the two networks constituting a cross-connected network, the common nodes are called cross-linked nodes.We empirically investigated six systems, and studied their common properties, find that the sum of the importance difference of all the cross-point in the two netwoks becomes lower when the ratio of the number of cross-point to total points becomes greater, and their relationship can be fitted by SPL in log-log coordinates. In order to verify the universality of this rule, we have been studied the degree distribution of cross-point, find that the degree distribution of cross-point of th six system can be expressed by SPL, namely, P( k≥k')∝(k'+α) ?γ,and the two parametersαandγbecome lower respectively when the sum of the importance difference of all the cross-linked points in the two netwoks becomes greater , and can also be fitted by SPL in log-log coordinates.We generate network in the base of empirical parameters in the numerical simulation, and put forward two hypothesises. First: the smaller of the difference functionδ, the greater probability of cross-linked of the two networks.Second: the smaller of the difference functionδ, the greater probability of the small value of the importance difference of cross-point i ; the greater of the difference functionδ, the greater probability of the great value of the importance difference of cross-point i. Changing the difference functionδ,we obtain the relation of the ratio of the number of cross-linked points to total points and the sum of the importance difference of all the cross-point in the two netwoks and find that it is in a good agreement with the empirical ones.we propose a very simplified model,that is, considering the degree distribution and the total number of nodes of the two networks are all the same, and the selection of cross-point satisfy a condition that the difference between the uper and the lower network there is invariability. Through the analysis ,We obtain the relationship about the ratio of the number of cross-point to total points and the sum of the importance difference of all the cross-point in the two netwoks and then draw their graph ,which is in a good agreement with the empirical and numerical simulation. We also study the degree distribution of cross-point,and find that they also satisfy the function of SPL, and the two parameter and the sum of the importance difference of all the cross-linked points can be fitted by SPL in log-log coordinates , which is in a good agreement with the empirical ones.At the end of the thesis we report an investigation on fruit nutritive factor network, in the view of complex network.we first propose some important properties include the node-weight distribution, act-weight distribution and the total node-weight distribution. These distribution show important information about the competition. Then we obtain two conclousions. The first important conclusion shown in the system is that the node- weight distribution and total node-weight distribution usually take so-called shifted power law func-tion forms. The key parameters,αandγ, may take very different values. However, the act-weight distribution may take a normal form.Another conclu- sion is that in some real world networks the degree and act-degree may show impulsive-spectrum like distributions such as this network, the distribution forms can not be described by eithe rpower law or normal functions.