基于自然数整除网络的素数与合数模式
Patterns of Primes and Composites from Divisibility Network of Natural Numbers
摘要：
我们提出的模式下的一些性质的自然数，使用复杂网络的框架。所使用的网络是可除性网络，其中每个节点具有作为自然数之一的固定身份，并且节点之间的连接是基于数之间的可除性模式进行的。我们推导出该网络的中心性措施的地板功能和除数函数的解析表达式。我们验证这些措施的帮助下，利用网络的邻接矩阵的标准方法。因此，从我们的研究中，网络的度量如何与素数和合数的行为模式相关变得显而易见。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
