带权超网络的度量方法及其性质

超网络是较通常意义上的复杂网络更为复杂的网络，该网络的每一条超边能连接任意多个节点的特性使其比复杂网络能更好地描述真实世界中的复杂系统。针对现有超网络研究中对超网络度量方法的缺陷与不足，提出了一种超网络度量方法——超网络维数（HD），即为所有超边包含的节点权重之和与对应超边权重乘积和的对数值和节点权重之和与超边权重之和乘积对数值的比值的两倍。超网络维数可以应用于节点权重与超边权重为正实数、负实数、纯虚数，乃至复数等多种不同数值类型的带权超网络中。最后给出了超网络维数的若干性质。

Measure method and properties of weighted hypernetwork

Hypernetwork is a kind of networks which is more complex than the ordinary complex network. Hypernetwork can describe complex system existing in the real world more appropriately than complex network since every hyperedge of it can connect any number of nodes. A new method to measure hypernetwork-Hypernetwork Dimension (HD) was proposed aiming to the shortcomings and deficiencies of existing measure method of hypernetwork. Hypernetwork dimension was expressed as twice as much as the ratio of the logarithm of the sum of all nodes' weights and product of corresponding hyperedge's weight in all hyperedges to the logarithm of the product of sum of hyperedges' weights and sum of nodes' weights. The hypernetwork dimension was able to be applied to the weighted hyperworks with many different numerical types of both nodes' weights and hyperedges' weights, such as positive real numbers, negative real numbers, pure imaginary numbers, and even complex numbers. Finally, several important properties of the proposed hypernetwork dimension were discussed.