Friedkin-Johnsen Model for Opinion Dynamics on Signed Graphs

TL;DR

This paper models opinion dynamics on signed social networks using the Friedkin-Johnsen model, introducing efficient algorithms for analysis and optimization, validated on large real-world networks.

Contribution

It offers a novel interpretation of equilibrium opinions via random walks on signed graphs and develops scalable algorithms for analysis and opinion optimization.

Findings

Effective algorithms for signed Laplacian systems.

Scalable methods tested on networks with over 20 million nodes.

Theoretical insights linking random walks and opinion equilibrium.

Abstract

A signed graph offers richer information than an unsigned graph, since it describes both collaborative and competitive relationships in social networks. In this paper, we study opinion dynamics on a signed graph, based on the Friedkin-Johnsen model. We first interpret the equilibrium opinion in terms of a defined random walk on an augmented signed graph, by representing the equilibrium opinion of every node as a combination of all nodes' internal opinions, with the coefficient of the internal opinion for each node being the difference of two absorbing probabilities. We then quantify some relevant social phenomena and express them in terms of the $\ell_2$ norms of vectors. We also design a nearly-linear time signed Laplacian solver for assessing these quantities, by establishing a connection between the absorbing probability of random walks on a signed graph and that on an associated unsigned graph. We further study the opinion optimization problem by changing the initial opinions of a fixed number of nodes, which can be optimally solved in cubic time. We provide a nearly-linear time algorithm with error guarantee to approximately solve the problem. Finally, we execute extensive experiments on sixteen real-life signed networks, which show that both of our algorithms are effective and efficient, and are scalable to massive graphs with over 20 million nodes.