# On the Analysis of the DeGroot-Friedkin Model with Dynamic Relative Interaction Matrices

arXiv: https://arxiv.org/abs/1703.04901 · HTML: https://mlsanity.com/paper/1703.04901/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [Initialisation and Network Effects in Decentralised Federated Learning](https://mlsanity.com/paper/2403.15855/) (2024)

## Abstract (arXiv)

This paper analyses the DeGroot-Friedkin model for evolution of the individuals' social powers in a social network when the network topology varies dynamically (described by dynamic relative interaction matrices). The DeGroot-Friedkin model describes how individual social power (self-appraisal, self-weight) evolves as a network of individuals discuss a sequence of issues. We seek to study dynamically changing relative interactions because interactions may change depending on the issue being discussed. In order to explore the problem in detail, two different cases of issue-dependent network topologies are studied. First, if the topology varies between issues in a periodic manner, it is shown that the individuals' self-appraisals admit a periodic solution. Second, if the topology changes arbitrarily, under the assumption that each relative interaction matrix is doubly stochastic and irreducible, the individuals' self-appraisals asymptotically converge to a unique non-trivial equilibrium.