# Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach

## TL;DR

This paper introduces Opinion Centrality, a new measure for multiplex networks based on opinion propagation dynamics, formulated through convex optimization, and demonstrates its unique properties and differences from existing measures.

## Contribution

It proposes a novel opinion-based centrality measure for multiplex networks derived from a convex optimization framework, highlighting nodes' influence on opinion spread.

## Key findings

- Opinion centrality is negatively correlated with existing measures.
- It emphasizes different nodes compared to traditional centrality metrics.
- The measure is validated on both toy and real-world networks.

## Abstract

Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition.