论文标题
来自自然数的划分网络的素数和复合材料的模式
Patterns of Primes and Composites from Divisibility Network of Natural Numbers
论文作者
论文摘要
我们使用复杂网络的框架介绍了自然数的某些属性的基础模式。所使用的网络是一个划界网络，其中每个节点具有固定的身份，作为自然数之一，并且节点之间的连接是根据数字之间的划分模式进行的。我们根据地板函数和除数功能来得出该网络中心度测量的分析表达式。我们借助标准方法来验证这些度量，这些方法利用网络的邻接矩阵。因此，从我们的研究中可以看出，网络的度量与素数和综合数字行为的模式如何相关。
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the connections among the nodes are made based on the divisibility pattern among the numbers. We derive analytical expressions for the centrality measures of this network in terms of the floor function and the divisor functions. We validate these measures with the help of standard methods which make use of the adjacency matrix of the network. Thus how the measures of the network relate to patterns in the behaviour of primes and composite numbers becomes apparent from our study.
