Investigación

 

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

 

J. Acosta-Elías^a, P. D. Arjona-Villicaña^a, and L. Moldes-Navarro^b

 

^a Universidad Autónoma de San Luis Potosí, Salvador Nava s/n, Zona Universitaria, CP 78290, San Luis Potosí, SLP, México, e-mail: jacosta@uaslp.mx

^b Universitat Politècnica de Catalunya, Campus Nord UPC, Jordi Girona 1-3, 08034 Barcelona Spain.

 

Received 7 February 2012.
Accepted 22 January 2014.

 

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.

Keywords: Complex networks.

 

PACS: 89.75.-k; 64.60.aq

 

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Acknowledgments

The authors would like to thank the Universidad Autónoma de San Luis Potosí, the Universidad Politécnica de Catalunya and Mexico's CONACYT for its support.

 

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