Importance of extremists for the structure of social networks.

The structure and the properties of complex networks essentially depend on the way nodes get connected to each other. We assume here that each node has a feature which attracts the others. We model the situation by assigning two numbers to each node, omega and alpha, where omega indicates some property of the node and alpha the affinity towards that property. A node A is more likely to establish a connection with a node B if B has a high value of omega and A has a high value of alpha. Simple computer simulations show that networks built according to this principle have a degree distribution with a power-law tail, whose exponent is determined only by the nodes with the largest value of the affinity alpha (the "extremists"). This means that the extremists lead the formation process of the network and manage to shape the final topology of the system. The latter phenomenon may have implications in the study of social networks and in epidemiology.