Priority weighted BA random graph model

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 priority weighted 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 by priority selected different edges to connected to the different vertices in the system, and (iii) new vertices attach preferentially to sites that are already well connected. A model based on these three ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.