Signed DeGroot-Friedkin Dynamics with Interdependent Topics

TL;DR

This paper extends DeGroot-Friedkin social power dynamics to signed influence networks with interdependent topics, providing explicit conditions for convergence and classifying limiting power configurations.

Contribution

It introduces a multi-topic signed influence framework with structural conditions for dynamics reduction and analyzes robustness and effects of losing common eigenvector structure.

Findings

Dynamics are globally convergent under certain conditions.

Limiting social power configurations are classified into three types.

The model remains robust under small perturbations of logic matrices.

Abstract

This paper investigates DeGroot-Friedkin (DF) dynamics over signed influence networks with interdependent topics. We propose a multi-topic signed framework that combines repelling interpersonal interactions with cross-issue self-appraisal, examining how antagonism and topic interdependence shape the evolution of agent-level social power. When the logic matrices (for topic interdependence) of all agents share a common dominant left eigenvector, we identify structural conditions under which the original dynamics admit an exact reduction to an explicit scalar DF map. This yields a complete classification of limiting social power configurations into pluralistic, mixed, and vertex-dominant types. In all three cases, the dynamics are globally convergent, and in the first two the ordering induced by the interaction centrality is preserved. We further show local robustness under small heterogeneous perturbations of the logic matrices. We also clarify what changes when this common-eigenvector structure is lost. These results extend signed social power dynamics beyond the standard nonnegative scalar setting and shed light on the robustness and scope of centrality-based social power formation in multi-topic signed influence systems.