近日，奥地利中欧大学的Albert-László Barabási及其研究小组取得一项新进展。经过不懈努力，他们揭示物理性对网络结构的影响。相关研究成果已于2023年11月6日在国际知名学术期刊《自然—物理学》上发表。

该研究团队创新性地引入了一个元图的概念，帮助他们精确映射了线性物理网络与独立集之间的关系，这是图论领域的一个核心概念。通过这一映射，研究人员得以深入解析物理效应的起源和堵塞转变的出现，进而揭示出物理性对网络结构的深刻影响，即使在链路总量可以忽略不计的情况下。为了验证这一理论的实用性，研究人员构建了多个真实物理网络的元图，并成功预测了与经验数据一致的功能特征，如脑连接体中的突突触形成。

这些研究成果强调了要充分理解真正复杂网络的演化和行为，必须充分量化和考虑物理实体的作用。因为物理网络是由物理实体构成的系统，所以传统的基于图的方法无法全面捕获这些实体的特性和相互作用。因此，理论工作的新方向是引入元图技术等更先进的分析工具，以更准确地揭示物理实体对网络结构的影响。

据悉，随着物理网络详细映射的出现，例如大脑连接体、血管网络或超材料中的复合网络等，其中的节点和链路作为物理实体，已暴露出当前网络科学工具集的局限性。链路的物理特性引入了一种非交叉条件，这种条件深刻地影响着网络的演化和结构，然而，这一关键信息仅凭邻接矩阵（作为所有基于图的方法的起点）是无法有效捕捉的。

附：英文原文

Title: Impact of physicality on network structure

Author: Psfai, Mrton, Szegedy, Balzs, Bai, Iva, Blagojevi, Luka, Abrt, Mikls, Kertsz, Jnos, Lovsz, Lszl, Barabási, Albert-László

Issue&Volume: 2023-11-06

Abstract: The emergence of detailed maps of physical networks, such as the brain connectome, vascular networks or composite networks in metamaterials, whose nodes and links are physical entities, has demonstrated the limits of the current network science toolset. Link physicality imposes a non-crossing condition that affects both the evolution and the structure of a network, in a way that the adjacency matrix alone—the starting point of all graph-based approaches—cannot capture. Here, we introduce a meta-graph that helps us to discover an exact mapping between linear physical networks and independent sets, which is a central concept in graph theory. The mapping allows us to analytically derive both the onset of physical effects and the emergence of a jamming transition, and to show that physicality affects the network structure even when the total volume of the links is negligible. Finally, we construct the meta-graphs of several real physical networks, which allows us to predict functional features, such as synapse formation in the brain connectome, that agree with empirical data. Overall, our results show that, to understand the evolution and behaviour of real complex networks, the role of physicality must be fully quantified. Physical networks are systems composed of physical entities, which conventional graph-based approaches fail to capture. Theoretical work now introduces a meta-graph technique to uncover the impact of physicality on the structure of networks.

DOI: 10.1038/s41567-023-02267-1

Source: https://www.nature.com/articles/s41567-023-02267-1