一个新的一般确定性分层网络族
A new general family of deterministic hierarchical networks
摘要：
众所周知，许多模拟现实生活中复杂系统的网络都是小词（大的局部聚类和小直径）和无标度（度分布的幂律）的，而且它们通常也是分层的。虽然大多数的模型是基于随机方法，最近已经提出了一些确定性的建设，因为这允许更好地计算其属性。这里提出了一种新的确定性的分层网络，它概括了大多数以前的建议，如所谓的二叉树。所获得的图可以被看作是字母表上的图（其中顶点用给定字母表的单词标记，并且边由与不同单词相关的特定规则定义）。这使我们能够表征它们的主要距离相关参数，如半径和直径。此外，作为副产品，一个有效的最短路径的本地算法。
英文摘要：
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of the models are based on stochastic methods, some deterministic constructions have been recently proposed, because this allows a better computation of their properties. Here a new deterministic family of hierarchical networks is presented, which generalizes most of the previous proposals, such as the so-called binomial tree. The obtained graphs can be seen as graphs on alphabets (where vertices are labeled with words of a given alphabet, and the edges are defined by a specific rule relating different words). This allows us the characterization of their main distance-related parameters, such as the radius and the diameter. Moreover, as a by product, an efficient shortest-path local algorithm is proposed.
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。
