论文标题
具有分形形态的空间系统的网络效率：几何图方法
Network efficiency of spatial systems with fractal morphology: a geometric graphs approach
论文作者
论文摘要
空间网络的功能特征取决于拓扑结构和物理结构之间的非平凡关系。在这里，我们探讨了与径向对称性和分形形态无序的空间网络的关系。在几何图方法下，我们量化了从中心到周长以及整个网络结构的系统中信息交换的有效性。我们主要考虑两个范式的分形形成模型，弹道聚集和扩散限制的聚集模型，以及互补的，viscek和Hexaflake分形，以及Kagome和Hexagonal Lattices。首先，我们表明复杂的树形态比常规配置具有重要的优势，例如不同分形维度的不变结构成本。此外，尽管已知这些系统在空间中是不含规模的，但它们具有欧几里得连接参数不同值的界限分布，因此并不代表普通的无标度网络。最后，与常规结构相比，分形树是脆弱的，总体效率低下，但是，我们表明这种效率可以与坚固的六角形晶格相似，仅考虑了第一邻居以外的欧几里得连接性非常短，就可以以类似的成本。
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal morphology. Under a geometric graphs approach, we quantify the effectiveness of the exchange of information in the system from center to perimeter and over the entire network structure. We mainly consider two paradigmatic models of disordered fractal formation, the Ballistic Aggregation and Diffusion-Limited Aggregation models, and complementary, the Viscek and Hexaflake fractals, and Kagome and Hexagonal lattices. First, we show that complex tree morphologies provide important advantages over regular configurations, such as an invariant structural cost for different fractal dimensions. Furthermore, although these systems are known to be scale-free in space, they have bounded degree distributions for different values of an euclidean connectivity parameter and, therefore, do not represent ordinary scale-free networks. Finally, compared to regular structures, fractal trees are fragile and overall inefficient as expected, however, we show that this efficiency can become similar to that of a robust hexagonal lattice, at a similar cost, by just considering a very short euclidean connectivity beyond first neighbors.
