PROPERTIES OF AN EVOLVING DIRECTED NETWORK WITH LOCAL RULES AND INTRINSIC VARIABLES

We present a simple model of an evolving directed network based on local rules. It leads to a complex network with the properties of real systems, like scale-free distribution of outgoing and incoming connectivity, and a hierarchical structure. Each node is characterised by an intrinsic variable S, and the number of outgoing links k out . As a result of network evolution the number of nodes and links (as well as their location) changes in time. For critical values of control parameters there is a transition to a scale-free network. Results for connectivity distribution found analytically agree with numerical calculations. Our model also reproduces other nontrivial properties of real networks, e.g. a large clustering coefficient and weak correlations between the age of a node and its connectivity. We have discovered an unexpected phenomenon that noise can increase the value of the clustering coefficient, whose large value is characteristic for a regular network.