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The importance of non-hub elements

Low-degree nodes crucial to dynamical robustness of complex networks

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Graduate School of Information Science and Technology
Institute of Industrial Science
2012/04/19

It has recently become clear that many of the networks in the world around us, including cellular metabolic pathways, neuronal networks, the Internet, and even human relationships, are scale-free networks, composed of a few high-degree hub nodes with many connections and an overwhelming majority of low-degree nodes with few connections.

A complex network in which 75% of the nodes have been suppressed. (Left) Circle size indicates node degree. Hub nodes in the center are essential to maintaining network integrity. (Right) Circle size indicates oscillation amplitude. Peripheral low-degree nodes are highly important in maintaining network activity. Figures prepared using Pajek. c Gouhei Tanaka.

A complex network in which 75% of the nodes have been suppressed. (Left) Circle size indicates node degree. Hub nodes in the center are essential to maintaining network integrity. (Right) Circle size indicates oscillation amplitude. Peripheral low-degree nodes are highly important in maintaining network activity. Figures prepared using Pajek. c Gouhei Tanaka.

Research to date has clearly demonstrated the important role of hub nodes in determining the robustness of scale-free networks. However, the role of low-degree nodes in such networks remained unknown.

Project Associate Professor Gouhei Tanaka, Professor Kazuyuki Aihara and researchers at the University of Tokyo’s Institute of Industrial Science and Graduate School of Information Science and Technology have shown that the dynamical robustness of scale-free networks is highly dependent on low-degree nodes, and have developed a theoretical framework for understanding dynamical robustness.

The team used a coupled oscillator network, a scale-free network of synchronized oscillating nodes often used to model biological phenomena, in which suppressed nodes were not able to oscillate independently but are able to produce a weak oscillation through interaction with surrounding nodes. The researchers suppressed the activity of nodes in a random and in a targeted fashion, and found that targeted suppression of low-degree nodes rendered the network highly fragile and less able to maintain dynamical activity.

This result demonstrates the importance of low-degree nodes in determining network dynamical robustness in addition to the role of hub nodes in determining structural robustness. It is hoped that this research will be of use in design of smart power grids able to function in the face of disasters, and in the development of a fundamental framework for understanding the progression of illnesses affecting biological networks including those in the heart and nervous system.

(Public Relations Division: Euan McKay, Azusa Minamizaki)

Department release/press release (Japanese)

Paper

Gouhei Tanaka, Kai Morino, and Kazuyuki Aihara
“Dynamical robustness in complex networks: the crucial role of low-degree nodes,”
Scientific Reports Vol 2 article number 232. 25 January 2012. doi:10.1038/srep00232
Article link

Links

Institute of Industrial Science

Graduate School of Information Science and Technology

Laboratories for Mathematics, Lifesciences, and Informatics

Project Associate Professor Gouhei Tanaka

Professor Kazuyuki Aihara

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