Weighted Fitness Model in Complex Networks

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of three generic mechanisms: (i) networks expand continuously by the addition of new vertices, (ii) new vertex with different number edges of weighted selected that connected to different vertices in the system, and (iii) by the fitness probability Π_i that a new vertices attach preferentially to sites that are already well connected. Uncovering this fitter-gets-richer phenomenon can help us understand in quantitative terms the evolution of many competitive systems in nature and society and Internet.