# Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution

arXiv: https://arxiv.org/abs/1608.06850 · HTML: https://mlsanity.com/paper/1608.06850/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2016.

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

- [Unbiased Derivative Estimation for Stationary Mean of Parameterized Markov chains](https://mlsanity.com/paper/2606.11487/) (2026)

## Abstract (arXiv)

Influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes. In this paper, we consider an alternate model that treats individual opinions as spins in an Ising system at dynamic equilibrium. We formalize the textitIsing influence maximization problem, which has a natural physical interpretation as maximizing the magnetization given a budget of external magnetic field. Under the mean-field (MF) approximation, we present a gradient ascent algorithm that uses the susceptibility to efficiently calculate local maxima of the magnetization, and we develop a number of sufficient conditions for when the MF magnetization is concave and our algorithm converges to a global optimum. We apply our algorithm on random and real-world networks, demonstrating, remarkably, that the MF optimal external fields (i.e., the external fields which maximize the MF magnetization) shift from focusing on high-degree individuals at high temperatures to focusing on low-degree individuals at low temperatures. We also establish a number of novel results about the structure of steady-states in the ferromagnetic MF Ising model on general graph topologies, which are of independent interest.