common and unique network dynamics in football games足球比赛中常见的和独特的网络动力学.pdfVIP

Common and Unique Network Dynamics in Football Games Yuji Yamamoto1,2*, Keiko Yokoyama3,4 1 Research Center of Health, Physical Fitness and Sports, Nagoya University, Furo-cho, Chikusa, Nagoya, Japan, 2 Department of Psychology and Human Developmental Sciences, Nagoya University, Furo-cho, Chikusa, Nagoya, Japan, 3 Division of Applied Physics, Faculty of Engineering, Hokkaido University, Kita-ku, Sapporo, Hokkaido, Japan, 4 Japan Society for the Promotion of Science, 5-3-1, Koujimachi, Chiyoda-ku, Tokyo, Japan Abstract The sport of football is played between two teams of eleven players each using a spherical ball. Each team strives to score by driving the ball into the opposing goal as the result of skillful interactions among players. Football can be regarded from the network perspective as a competitive relationship between two cooperative networks with a dynamic network topology and dynamic network node. Many complex large-scale networks have been shown to have topological properties in common, based on a small-world network and scale-free network models. However, the human dynamic movement pattern of this network has never been investigated in a real-world setting. Here, we show that the power law in degree distribution emerged in the passing behavior in the 2006 FIFA World Cup Final and an international ‘‘A’’ match in Japan, by describing players as vertices connected by links representing passes. The exponent values c *3:1 are similar to the typical values that occur in many real-world networks, which are in the range of 2 vc v3, and are larger than that of a gene transcription network, c *1. Furthermore, we reveal the stochastically switched dynamics of the hub player throughout the game as a unique feature in football games. It suggests that this feature could result not only in securing