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 \textit{Ising 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) exhibit a phase transition from focusing on high-degree individuals at high temperatures to focusing on low-degree individuals at low temperatures.

The paper studies the influence maximization using the Ising network model. However, the motivation for using Ising network model for opinion dynamics is not well motivated. Why do we need to use the Ising model? It is less convincing by just saying that this model can capture the steady-state of the opinion dynamics. Some other model can also consider the steady state. For example, how does it compare with prior work such as [1].

Influence Maximization is the task of selecting optimal nodes maximising the influence spread in social networks. This study proposes a Discretized Quantum-based Salp Swarm Algorithm (DQSSA) for optimizing influence diffusion in social networks. By discretizing meta-heuristic algorithms and infusing them with quantum-inspired enhancements, we address issues like premature convergence and low efficacy. The proposed method, guided by quantum principles, offers a promising solution for Influence Maximisation. Experiments on four real-world datasets reveal DQSSA's superior performance as compared to established cutting-edge algorithms.

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 \textit{Ising 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) exhibit a phase transition from focusing on high-degree individuals at high temperatures to focusing on low-degree individuals at low temperatures.