用矩阵权重建模多维交互，揭示复杂系统新稳态
Matrix-weighted networks for modeling multidimensional dynamics
- 用矩阵替代标量表示边权重，捕捉多维交互关系
- 发现网络一致性导致非平凡稳态，扩展社区与结构平衡概念
- 适用于社交、生物等多维动态系统研究
网络是建模复杂系统中相互作用的强大工具。传统网络使用标量边权重，但许多现实系统涉及多维交互。例如，在社交网络中，个体常有多个相互关联的观点，这些观点会影响其他个体的不同观点，更适合用矩阵表示。本文提出一种新型通用框架：矩阵加权网络（MWNs），构建了MWNs的数学基础，并研究了其中的一致性动态和随机游走。结果表明，MWNs的一致性会产生非平凡的稳态，推广了传统网络中社区和结构平衡的概念。
原文摘要 · Abstract (English)
Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often have multiple interconnected opinions that can affect different opinions of other individuals, which can be better characterized by matrices. We propose a novel, general framework for modeling such multidimensional interacting dynamics: matrix-weighted networks (MWNs). We present the mathematical foundations of MWNs and examine consensus dynamics and random walks within this context. Our results reveal that the coherence of MWNs gives rise to non-trivial steady states that generalize the notions of communities and structural balance in traditional networks.
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