Structure Properties of Koch Networks Based on Networks Dynamical Systems

TL;DR

This paper presents a labeling algorithm for Koch networks that enables efficient shortest path routing, betweenness centrality calculation, and community structure analysis based on network dynamics.

Contribution

It introduces a novel labeling scheme for Koch networks that simplifies routing and centrality computations, and explores community structure through resistor network analogies.

Findings

Efficient shortest path routing using labels

Explicit betweenness centrality formulas derived

Community structure analyzed via resistor network properties

Abstract

We introduce an informative labeling algorithm for the vertices of a family of Koch networks. Each of the labels is consisted of two parts, the precise position and the time adding to Koch networks. The shortest path routing between any two vertices is determined only on the basis of their labels, and the routing is calculated only by few computations. The rigorous solutions of betweenness centrality for every node and edge are also derived by the help of their labels. Furthermore, the community structure in Koch networks is studied by the current and voltage characteristics of its resistor networks.