复杂网络中格林函数的多维动力学中心性

中文摘要 AI 辅助

传统的中心性度量提供了节点重要性的紧凑描述，但它们强调特定的结构关系，并不能直接解析动力学扰动响应的时间与谱组织。基于线性化网络系统的格林函数，我们发展了一个用于动力学节点表征的多维框架。从同一响应函数中，我们提取三个互补指标——影响力、效率与失真——分别量化累积响应强度、响应的时间速率与谱集中度，以及一个贡献矩阵，将这些量分解为源-目标路径。作为数值演示，我们将该框架应用于异构巴拉巴西-阿尔伯特网络上的加权藏本-坂口动力学。这三个指标通过扰动响应的互补维度区分植入的动力学节点类别，同时与传统拓扑中心性保持强耦合。这些结果展示了如何将共同的动力学响应分解为不同的、物理上可解释的特征，而非由单一聚合描述符表示。最后，我们讨论了线性响应假设的范围与局限性，以及向时间依赖和非线性情形的扩展。

英文摘要

Conventional centrality measures provide compact descriptions of node importance, but they emphasize specific structural relations and do not directly resolve the temporal and spectral organization of dynamical perturbation responses. Building on the Green function of a linearized networked system, we develop a multidimensional framework for dynamical node characterization. From the same response function, we extract three complementary indicators---Influence, Efficiency, and Distortion---that quantify cumulative response strength, temporal rate of response, and spectral concentration, respectively, together with a contribution matrix that resolves these quantities into source--target pathways. As a numerical demonstration, we apply the framework to weighted Kuramoto--Sakaguchi dynamics on heterogeneous Barabási--Albert networks. The three indicators distinguish implanted dynamical node classes through complementary dimensions of the perturbation response, while remaining strongly coupled to conventional topological centralities. These results demonstrate how a common dynamical response can be decomposed into distinct, physically interpretable characteristics rather than represented by a single aggregate descriptor. We finally discuss the scope and limitations of the linear-response assumption and extensions to time-dependent and nonlinear regimes.

发表机构

• Xi’an Jiaotong-Liverpool University（西交利物浦大学）
• University College London（伦敦大学学院）

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