Modeling Of Random Pseudofractal Networks

The complex network is a tool to describe a wide range of systems in nature and society. The small-world and scale-free in many complex networks have attached many scientists’attentions and complex networks have got many achievements such as ER model, WS model and BA model.Setting up the evolutive network models of scale-free network is an important investigative field. Some deterministic scale-free networks are proposed such as hi-erarchical network、pseudofractal scale-free web and Koch network. In this paper, we focus on pseudofractal network models, propose a Koch network based on the triangle and some random pseudofractal networks based on a new generation mech-anism which is called triangle preferential attachment. We analyze these networks by the numerical and analytical approaches:(1) We propose a new way to map Koch curves into a new deterministic network. We call it Koch network based on the triangle. The triangles in the Koch curves are mapped to nodes, which are connected to one another if their corresponding triangles in the Koch curves have a common edge. The analytical result shows the degree distribution has a power-law tail.(2) In order to incorporate randomness into the deterministic networks, we propose two random pseudofractal networks based on a new generation mechanism which is called triangle preferential attachment and the triangle distribution as a new statistic. The analytical results show the triangle distribution and the degree distribution of two random pseudofractal networks both have a power-law tail and the clustering coefficient of the random pseudofractal network based on the node with the triangle preferential attachment is high.(3) We propose two random pseudofractal networks based on the polygon pref-erential attachment and the polygon distribution as a new statistic. The analytical results show the polygon distribution and the degree distribution both have a power-law tail.