Competition and multiscaling in evolving networks

The rate at which nodes in a network increase their connectivity depends on their fitness to compete for links. For example, in social networks some individuals acquire more social links than others, or on the www some webpages attract considerably more links than others. We find that this competition for links translates into multiscaling, i.e. a fitness dependent dynamic exponent, allowing fitter nodes to overcome the more connected but less fit ones. Uncovering this fitter-gets-richer phenomena can help us understand in quantitative terms the evolution of many competitive systems in nature and society. PACS numbers: 5.65+b, 89.75-k, 89.75Fb, 89.75Hc. Typeset using REVTEXThe complexity of many systems can be attributed to the interwoven web in which their constituents interact with each other. For example, the society is organized in a social web, whose nodes are individuals and links represent various social interactions, or the www forms a complex web whose nodes are documents and links are URLs. While for a long time these networks have been modeled as completely random 1, 2, recently there is increasing