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Thursday, July 21, 2005
11:00 AM - 12:00 PM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

Length of the Optimal Path in Disordered Complex Network

Lidia A. Braunstein
University of Mar Del Plata

We study the optimal distance in random networks in presence of disorder. The optimal distance between two nodes is the length of the path for which the sum of cost along the path is a minimum.The disorder is implemented by assigning costs to the each link of the network. The costs are taken from a broad distribution. We find theoretically, using percolation theory that in the strong disorder limit the average optimal path length scales with the system size N as a power law both for Erd\H{o}s-R\'enyi (ER) and scale free (SF) networks. These results were confirmed numerically. Thus, by increasing the disorder, the small world behavior is destroyed. We also found that for weak disorder the average optimal path length scales as log N.