# Fast Evaluation for Relevant Quantities of Opinion Dynamics

arXiv: https://arxiv.org/abs/2101.08143 · HTML: https://mlsanity.com/paper/2101.08143/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2021.

## Built on by (most cited first, 2 of 2)

- [Adversaries with Limited Information in the Friedkin--Johnsen Model](https://mlsanity.com/paper/2306.10313/) (2023)
- [Sublinear-Time Algorithms for Diagonally Dominant Systems and Applications to the Friedkin-Johnsen Model](https://mlsanity.com/paper/2509.13112/) (2025)

## Abstract (arXiv)

One of the main subjects in the field of social networks is to quantify conflict, disagreement, controversy, and polarization, and some quantitative indicators have been developed to quantify these concepts. However, direct computation of these indicators involves the operations of matrix inversion and multiplication, which make it computationally infeasible for large-scale graphs with millions of nodes. In this paper, by reducing the problem of computing relevant quantities to evaluating ℓ2 norms of some vectors, we present a nearly linear time algorithm to estimate all these quantities. Our algorithm is based on the Laplacian solvers, and has a proved theoretical guarantee of error for each quantity. We execute extensive numerical experiments on a variety of real networks, which demonstrate that our approximation algorithm is efficient and effective, scalable to large graphs having millions of nodes.