Characteristics of a preferentially-attached network grown from a small world

摘要

We introduce a model for a preferentially-attached network that was grown from a small-world network. Here, the average path length and the clustering coefficient are estimated, and the topological properties of the modeled networks are compared as the initial conditions are changed. As a result, the topological properties of the initial network are shown to remain even after the network growth. However, the vulnerability of each to preferentially-attached nodes being added is not the same. The average path length is found to decrease rapidly as the ratio of preferentially-attached nodes increases, and the characteristics of the initial network easily disappears. On the other hand, the clustering coefficient of the initial network slowly decreases with the ratio of preferentiallyattached nodes, but its clustering characteristic remains much longer.