Analyses On The Properties Of Traffic Behaviors For Random Walks On Complex Networks

Researches of complex networks have received more significant attention in recent years. Researches of complex networks have very important value. The main subject of studying complex networks is to understand the function of the real network system through studying the characteristics of traffic dynamic processes taking place on networks. Academician have put forward many methods to study the characteristics of traffic dynamics. In this paper, we use random walks model to study the properties of complex networks. Random walks model is very easy, which maximum covers many traffic processes in real life, such as:epidemic spreading, transportation, network exploring, and so on. The main work for this paper is as follows.(1)The characteristics of traffic dynamics is investigated on general binary networks. In our paper, we deduce the exact solution of MFPT by a much cleaner approach through analyzing the properties of general binary networks and combining with the inside knowledge of spectral graph theory. Then we present the relation properties of MFPT and network structure properties according to the analysis results of Cauchy inequality.(2)The characteristics of traffic dynamics is investigated on Deterministic Weighted Scale-Free Small-World Networks. Researches of random walks on deterministic weighted scale-free small-world networks with a perfect trap is done. Evolution equations of FPT is given as the structure of networks changing, the formulation so ATT also deduced further. The result of ATT show that MFPT grows super-linearly with the growth of the network.(3)The characteristics of traffic dynamics is investigated on uncorrelated weighted networks. we analytically derive the stationary distribution for two different types of random walks on uncorrelated weighted networks. Then we can obtain the explicit expression of MFRT. The results are verified by computer simulation.(4)The characteristics of cover time of random walks is investigated on weighted networks. cover time have very highly worth researching and realizing. The efficiency of traversal for networks edge or node through different random walks rules is presented by computer simulation, which presents the effects of efficiency traversal under different network structures.