Weighted Scale-Free 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 scale-free power-law distribution. This feature was found to be a consequence of three generic mechanisms: (i) networks expand continuously by attaching addition of new vertices, (ii) new vertex with different number edges of weighted selected connectioned to 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 indicate that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.