Modeling real-world networks with degree-preserving processes
Visiting speaker
Zoltán Toroczkai
Professor, University of Notre Dame
Past Talk
Virtual talk
Thursday
Feb 2, 2023
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11:00 am
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177 Huntington Ave.
11th floor
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Modeling real-world networks is a key focus area of Network Science. I will first provide a brief overview into the state-of-the-art of network modeling, then turn to the discussion of network evolution models. In current network-evolution models, the degree of each node varies or grows arbitrarily, yet there are many networks for which a different description is required. In some networks, node degree saturates, such as the number of active contacts of a person, and in some it is fixed, such as the valence of an atom in a molecule. I will introduce a novel family of network growth processes that preserve node degree (DPG), resulting in structures substantially different from those reported previously. We demonstrated that, despite it being an NP (non-deterministic polynomial time)-hard problem in general, the exact structure of most real-world networks can be generated from degree-preserving growth. We also show that this process can create scale-free networks with arbitrary exponents, however, without preferential attachment. If preferential attachment is an effective rich-gets-richer mechanism applied to connectivity formation, then degree-preserving growth is a type of “tinkering” mechanism, a property observed in many real systems, e.g., by the Nobel Laurate F. Jacob in: “Evolution and Tinkering”, Science, 196, 1161 (1977)). Finally, I will present applications of DPG to epidemics control via network immunization, viral marketing, knowledge dissemination, the design of molecular isomers with desired properties and to a problem in number theory.

About the speaker
About the speaker
Zoltán Toroczkai received his Ph.D. degree in theoretical physics from Virginia Tech, in 1997. After a post-doctoral position at University of Maryland, he became a Director Funded Fellow at the Los Alamos National Laboratory (LANL). He was then converted into a Research Staff Member in the Complex Systems Group in 2002 and became the Deputy Director of the Center for Nonlinear Studies, LANL, 2004-06. In 2006, he joined the Department of Physics at University of Notre Dame, where he is currently a Professor and a Concurrent Professor with the Department of Computer Science and Engineering. His research interests include statistical physics, nonlinear dynamical systems, complex networks, foundations of computing, and brain neuronal systems. He was elected APS Fellow in 2012 upon nomination by GSNP “For his contributions to the understanding of the statistical physics of complex systems, and in particular for his discoveries pertaining to the structure and dynamics of complex networks.”
Zoltán Toroczkai received his Ph.D. degree in theoretical physics from Virginia Tech, in 1997. After a post-doctoral position at University of Maryland, he became a Director Funded Fellow at the Los Alamos National Laboratory (LANL). He was then converted into a Research Staff Member in the Complex Systems Group in 2002 and became the Deputy Director of the Center for Nonlinear Studies, LANL, 2004-06. In 2006, he joined the Department of Physics at University of Notre Dame, where he is currently a Professor and a Concurrent Professor with the Department of Computer Science and Engineering. His research interests include statistical physics, nonlinear dynamical systems, complex networks, foundations of computing, and brain neuronal systems. He was elected APS Fellow in 2012 upon nomination by GSNP “For his contributions to the understanding of the statistical physics of complex systems, and in particular for his discoveries pertaining to the structure and dynamics of complex networks.”