带权超网络的多重分形研究

Research on multi-fractals of weighted hypernetworks

超网络是较通常意义上的复杂网络更为复杂的网络,超网络维数是度量超网络的一种可行的方法.针对带权超网络中节点权重及超边权重可以分别为正实数、负实数、纯虚数及复数等多种不同的类型,首先给出了各种不同类型带权超网络的多重分形维数;然后讨论了带权超网络的多重分形特性;研究表明,在不同类型的带权超网络中,除节点权重及超边权重均为正实数及负实数的两种情形之外,其他类型的带权超网络均具有多重分形特性,且可以分为7个不同的类别,均分布于整个复平面;最后给出了所有这些带权超网络多重分形维数的解析表达式,并分析了这些带权超网络多重分形维数的若干重要性质.

Hypernetwork is a kind of network that is more complex than ordinary complex networks,while hypernetwork dimension is a feasible tool for measuring it.For the case that both node weight and hyperedge weight in weighted hypernetworks can value among positive real number,negative real number,pure imaginary number and complex number,etc.,fractal dimensions for various weighted hypernetworks is proposed and their multi-fractals are discussed.It is shown that among all types of weighted hypernetworks,except those with both node weight and hyperedge weight being positive or negative real numbers,other types of weighted hypernetworks share multi-fractals and can be divided into seven different categories that are all distributed in the entire complex plane.The analytic expressions of multi-fractal dimensions for all types of weighted hypernetworks are also presented.Finally,some important properties of the multi-fractal dimensions of these weighted hypernetworks are analyzed.