给出了超网络中点度、点超度、加权点度、边度、超边度、聚集系数、平均距离等拓扑特性的定义和计算公式。将电视节目定义为节点,将播出时间段定义为超边,采用超网络方法分析了电视节目的竞争关系。实证结果显示,这些统计属性的累计概率分布服从指数分布,说明多个随机因素的相互作用导致了该超网络的形成。其中,加权点度能够更好地描述超网络的竞争态势。较小的平均距离和较大的聚集系数表明该超网络符合小世界效应。这些拓扑指标能够较好地反映竞争超网络所具有的特点,方法同样适用于实证分析其它合作或竞争超网络。
The node degrees, weighted node degrees, node hyperdegrees, hyperedge degrees, hyperedge hyperdegrees, average distance and clustering coefficient are proposed in the paper. TV programs are defined as nodes and broadcasting time periods are defined as hyperedges. By using hypernetwork analysis of television programs competitive relationships, we find that the cumulative probability distributions can be described by an exponential distribution. It shows that random factors result in the formation of the hypernetwork. The competition of the supernetwork can be better described by weighted node degrees. The average distance is small and the clustering coefficient is large. These parameters conform to the characteristics of small-world network. These topological characteristics may be useful for the studies of competitive hypernetworks. The methods proposed can also be used for other empirical studies.
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