The impact of time delay in the connectivity distribution of complex networks generated using the Barabási-Albert model

Abstract

In the Barabási-Albert growth model for complex networks new nodes added to the network, obtain instant information from the entire network and employ preferential connectivity to select a node to establish a connection. In practice, information takes time to propagate from a sender to a receiver. We modify the Barabási-Albert model to include the time information takes to propagate between nodes. In the modified model a time delay is associated to the transmission of information and each new node must wait for a period of time to receive the network connectivity information. By adjusting this waiting time, different functional forms of the connectivity distribution are obtained. These connectivity distributions form a spectrum of functional forms which lie between two limiting cases: a power law distribution for large waiting times and an exponential distribution for short waiting times.