Modeling Of Scale-Free Networks Through Random Walk

Complex networks can describe a wide range of systems in nature and society. Such as citation networks, movie actor collaboration network, cellular networks,etc. In this papcr,we focus on modeling the complex networks through random walk, propose three meaningful evolving network models, and analyze the networks by the combined theoretical and analytical approach.(l)Considcr this question:two acquaintances make their friends know each other. We propose a model of relationship network with quadrilateral. Theoretical results show that the distribution has a power-law tail.(2)A collaboration network with two-way choice is proposed. A new member choose m members who he hope to collaborate preferentially. At the same time,every one of m members all have three choices:collaborate with the new member, intro-duce his collaborators to the new member, make no direct or indirect collaboration with the new member. Analytical results indicate that the strength and weight distributions have scale-free properties.(3)A bipartite model with doctor-drug is constructed. The top intra-degree represents how many kinds of drugs can be used together with some drug. The top inter-degree represents how many doctors prescribe some drug. The bottom inter-degree represents the sorts of drugs prescribed by a doctor. The results show that the three degree distributions of the network is scale-free.