Matrix-weighted networks for modeling multidimensional dynamics: theoretical foundations and applications to network coherence

Journal article

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 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 nontrivial steady states that generalize the notions of communities and structural balance in traditional networks.

Authors: Tian, Y; Kojaku, S; Sayama, H; Lambiotte, R

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review Letters
• Volume: 134
• Issue: 23
• Article number: 237401
• Publication date: 2025-06-13
• Acceptance date: 2025-05-21
• DOI: 10.1103/jw1k-6s7w
• EISSN: 1079-7114
• ISSN: 0031-9007
• Language: English
• Keywords: collective behavior in networks; network diffusion; network structure; topological tools; interconnected and interdependent networks; social networks; weighted networks; diffusion and random walks; networks analysis tools