The Results Of A Weighted Evolving Network Model With Intrinsic Strength

In recent years, complex networks have set off a wave of domestic and foreign research, andhave been strongly concerned by the researchers in many areas. From the mathematical point of view,many networks can be abstracted as a graph consisting of nodes and edges. In fact, weight is animportant ingredient of many real networks, and it is better to describe the real networks with weight.The empirical results show that these weighted networks exhibit complex topological propertiesobserved in real networks. So, there is a need for a modeling approach to complex networks that couldbetter characterize these topological features of real networks.In order to explore mechanism responsible for the phenomena of power-law in the weightednetworks, we present a general model for the growth of weighted networks, which is based on aweight and intrinsic strength driven dynamics and it also generates networks exhibiting the statisticalproperties observed in several real-world systems. Within this model we not only yields the scale-freebehavior for the weight, strength, degree and intrinsic strength distributions, but also we give theanalytical computation of the distributions of the strength and the degree, and we found the analyticalresults are good consistent with those of numerical simulation. Simultaneity, by way of contrastingour results with those of the random model, we found the preferential attachment is sufficient for thephenomena of scale-free of the weight, the strength, the degree and intrinsic strength distributions. Atlast, according to the numerical simulation, we get the relationship between the degree and thestrength, that is s k.