Effects Of Weight On Network Efficiency

Recently, much attention has been focused on weighted complex networks, which have widely used to describe complex systems. In weighted networks, the interactions of nodes are not the same as in unweighted networks, and instead, they are different from each other. We can read much new information from these differences, so it is essential to introduce weight into networks.Our research focus on how weight distribution exerts influence on networks'efficiency. Because of the restrictions on topology by using average shortest path length L and cluster coefficient C , Latora introduced efficiency to play the role of L and C to avoid these limitations, proposed the definition of efficiency based on dissimilarity weight and analyze the efficiency of different topology. Noting the difference between dissimilarity weight and similarity weight, we focus on efficiency of similarity weighted networks. The efficiency between two nodes equals to their link weight not the inverse. Since delta weight distribution cause small world effect and influence the dynamics of networks, this thesis focus on the effect of adjusting weight distribution.It should take into account the cost and efficiency to judge whether a method is realistic. In transportation, the minim spanning tree (MST) is the main roads of the entire network, and the infinite incipient percolation cluster (IIC) is the core road of the MST. So the total weight on MST can be viewed as transport cost. In this thesis we investigate the cost after weight redistribution and the usage of IIC.The study shows that under different topology structure, both the global and local efficiency are enhanced after weight redistribution. When we consider certain topology, its efficiency is enhanced as the incensement of probability while the cost is continue decreasing which suggests that the enhancement of efficiency does not at the cost of the expense of transportation. Meanwhile the usage of IIC is obviously increased after weight redistribution. The result of this thesis further determines the position and function, and provides a new angle to optimize weighted networks.