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Scale-Free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks | IEEE Journals & Magazine | IEEE Xplore

Scale-Free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks


Abstract:

The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study fi...Show More

Abstract:

The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where vertices are subject to white noise. We focus on the coherence of networks characterized in terms of the H2-norm, which quantifies how closely the agents track the consensus value. We first provide a lower bound of coherence of a network in terms of its average degree, which is independent of the network order. We then study the coherence of some sparse, scale-free real-world networks, which approaches a constant. We also study numerically the coherence of Barabási-Albert networks and high-dimensional random Apollonian networks, which also converges to a constant when the networks grow. Finally, based on the connection of coherence and the Kirchhoff index, we study analytically the coherence of two deterministically growing sparse networks and obtain the exact expressions, which tend to small constants. Our results indicate that the effect of noise on the consensus dynamics in power-law networks is negligible. We argue that scale-free topology, together with loopy structure, is responsible for the strong robustness with respect to noisy consensus dynamics in power-law networks.
Published in: IEEE Transactions on Cybernetics ( Volume: 50, Issue: 1, January 2020)
Page(s): 190 - 200
Date of Publication: 26 September 2018

ISSN Information:

PubMed ID: 30273162

Funding Agency:

Author image of Yuhao Yi
Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China
Yuhao Yi received the B.S. degree in computer science from Fudan University, Shanghai, China, in 2013, where he is currently pursuing the Ph.D. degree.
His current research interests include network science, distributed control, and spectral graph theory. His current research centers on analyzing and optimizing the performance of averaging consensus dynamics in large-scale networks.
Yuhao Yi received the B.S. degree in computer science from Fudan University, Shanghai, China, in 2013, where he is currently pursuing the Ph.D. degree.
His current research interests include network science, distributed control, and spectral graph theory. His current research centers on analyzing and optimizing the performance of averaging consensus dynamics in large-scale networks.View more
Author image of Zhongzhi Zhang
Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China
Zhongzhi Zhang received the B.Sc. degree in applied mathematics from Anhui University, Hefei, China, in 1997 and the Ph.D. degree in management science and engineering from the Dalian University of Technology, Dalian, China, in 2006.
From 2006 to 2008, he was a Post-Doctoral Research Fellow with Fudan University, Shanghai, China, where he is currently an Associate Professor with the School of Computer Science. He has publi...Show More
Zhongzhi Zhang received the B.Sc. degree in applied mathematics from Anhui University, Hefei, China, in 1997 and the Ph.D. degree in management science and engineering from the Dalian University of Technology, Dalian, China, in 2006.
From 2006 to 2008, he was a Post-Doctoral Research Fellow with Fudan University, Shanghai, China, where he is currently an Associate Professor with the School of Computer Science. He has publi...View more
Author image of Stacy Patterson
Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA
Stacy Patterson (M’13) received the M.S. and Ph.D. degrees in computer science from the University of California at Santa Barbara, Santa Barbara, CA, USA, in 2003 and 2009, respectively.
She is a Clare Boothe Luce Assistant Professor with the Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA. From 2009 to 2011, she was a Post-Doctoral Scholar with the Center for Control, Dynamical Systems and ...Show More
Stacy Patterson (M’13) received the M.S. and Ph.D. degrees in computer science from the University of California at Santa Barbara, Santa Barbara, CA, USA, in 2003 and 2009, respectively.
She is a Clare Boothe Luce Assistant Professor with the Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA. From 2009 to 2011, she was a Post-Doctoral Scholar with the Center for Control, Dynamical Systems and ...View more

Author image of Yuhao Yi
Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China
Yuhao Yi received the B.S. degree in computer science from Fudan University, Shanghai, China, in 2013, where he is currently pursuing the Ph.D. degree.
His current research interests include network science, distributed control, and spectral graph theory. His current research centers on analyzing and optimizing the performance of averaging consensus dynamics in large-scale networks.
Yuhao Yi received the B.S. degree in computer science from Fudan University, Shanghai, China, in 2013, where he is currently pursuing the Ph.D. degree.
His current research interests include network science, distributed control, and spectral graph theory. His current research centers on analyzing and optimizing the performance of averaging consensus dynamics in large-scale networks.View more
Author image of Zhongzhi Zhang
Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China
Zhongzhi Zhang received the B.Sc. degree in applied mathematics from Anhui University, Hefei, China, in 1997 and the Ph.D. degree in management science and engineering from the Dalian University of Technology, Dalian, China, in 2006.
From 2006 to 2008, he was a Post-Doctoral Research Fellow with Fudan University, Shanghai, China, where he is currently an Associate Professor with the School of Computer Science. He has published over 100 papers in international journals in the field of network modeling and dynamics. He has over 2300 ISI Web of Science citations with an H -index of 28 according to the Thomson Reuters. His current research interests include structural and dynamical properties of complex networks.
Dr. Zhang was a recipient of the Excellent Doctoral Dissertation Award of Liaoning Province, China, in 2007, the Excellent Post-Doctor Award of Fudan University in 2008, and the Shanghai Natural Science Award (third class) in 2013. He is a Committee Member of the Chinese Society of Complexity Science.
Zhongzhi Zhang received the B.Sc. degree in applied mathematics from Anhui University, Hefei, China, in 1997 and the Ph.D. degree in management science and engineering from the Dalian University of Technology, Dalian, China, in 2006.
From 2006 to 2008, he was a Post-Doctoral Research Fellow with Fudan University, Shanghai, China, where he is currently an Associate Professor with the School of Computer Science. He has published over 100 papers in international journals in the field of network modeling and dynamics. He has over 2300 ISI Web of Science citations with an H -index of 28 according to the Thomson Reuters. His current research interests include structural and dynamical properties of complex networks.
Dr. Zhang was a recipient of the Excellent Doctoral Dissertation Award of Liaoning Province, China, in 2007, the Excellent Post-Doctor Award of Fudan University in 2008, and the Shanghai Natural Science Award (third class) in 2013. He is a Committee Member of the Chinese Society of Complexity Science.View more
Author image of Stacy Patterson
Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA
Stacy Patterson (M’13) received the M.S. and Ph.D. degrees in computer science from the University of California at Santa Barbara, Santa Barbara, CA, USA, in 2003 and 2009, respectively.
She is a Clare Boothe Luce Assistant Professor with the Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA. From 2009 to 2011, she was a Post-Doctoral Scholar with the Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara. From 2011 to 2013, she was a Post-Doctoral Fellow with the Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa, Israel. Her current research interests include distributed systems, cloud computing, sensor networks, and Internet of Things.
Dr. Patterson was a recipient of the Viterbi Post-Doctoral Fellowship, the IEEE CSS Axelby Outstanding Paper Award, and the NSF CAREER Award.
Stacy Patterson (M’13) received the M.S. and Ph.D. degrees in computer science from the University of California at Santa Barbara, Santa Barbara, CA, USA, in 2003 and 2009, respectively.
She is a Clare Boothe Luce Assistant Professor with the Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA. From 2009 to 2011, she was a Post-Doctoral Scholar with the Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara. From 2011 to 2013, she was a Post-Doctoral Fellow with the Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa, Israel. Her current research interests include distributed systems, cloud computing, sensor networks, and Internet of Things.
Dr. Patterson was a recipient of the Viterbi Post-Doctoral Fellowship, the IEEE CSS Axelby Outstanding Paper Award, and the NSF CAREER Award.View more

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