The Department of Physics
at Northeastern University presents
NETWORK SCIENCE INSTITUTE SEMINAR
Self-Similar Complex Networks and Multiplexes
Marián Boguñá, Associate Professor
University of Barcelona, Spain
November 10, 2015
11:00 –11:45 a.m.
Refreshments will be available at 10:30 a.m.
Self-similarity is defined in a wide sense as the property of some systems to be, either exactly or statistically, similar to a part of themselves. This property is found in certain geometric objects that are intrinsically embedded in metric spaces, so that distance in the metric space gives a natural standard of measurement to uncover similar patterns at different observation scales. In complex networks, the definition of self-similarity is not obvious since many networks are not explicitly embedded in any physical geometry. In the absence of a natural geometry, the main problem in the definition of self-similarity stems from the fact that there is, a priori, no way to decide what is the part of the system that should be compared to (and look alike) the whole. In this sense, self-similarity is not an intrinsic property of the system but it is directly related to the specific procedure to identify the appropriate subsystem. In this talk, I will explain how to define self-similarity in ensembles of networks and multiplexes. Self-similarity has important implications in the global structure of networks and, in particular, in their vulnerability to failures of their constituents. For instance, self-similarity alone ‹independently of the divergence of the second moment of the degree distribution‹ explains the absence of a percolation threshold in random scale-free networks. In the case of self-similar multiplexes, we show that interlayer degree correlations can change completely their global connectivity properties, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary percolation properties of noninteracting networks.
Host: Dima Krioukov, Associate Professor