Characteristics of Preferentially Attached Network Grown from Small World

TL;DR

This paper investigates how initial small-world network properties influence the evolution of networks under preferential attachment, revealing that some properties persist while others change rapidly as new nodes are added.

Contribution

It introduces a model for growing networks from small-world structures and analyzes how initial topological features are affected by preferential attachment.

Findings

Average path length decreases rapidly with more preferentially attached nodes.

Initial clustering coefficients decline slowly, maintaining clustering characteristics longer.

Topological properties of the initial network can persist or change depending on the property.

Abstract

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