[Paper Review] Disabling External Influence in Social Networks via Edge Recommendation

Victor Amelkin, Ambuj K. Singh|arXiv (Cornell University)|Sep 24, 2017

Opinion Dynamics and Social Influence43 references3 citations

TL;DR

This paper introduces DIVER, a novel NP-hard problem that disables external influence in social networks by strategically recommending edges to counteract adversarial opinion manipulation. Using perturbation analysis of eigenvector centrality in Markov chains, the authors develop a pseudo-linear-time heuristic that efficiently restores the original asymptotic consensus value, achieving near-original states within 17 iterations (85 edges) in experiments.

ABSTRACT

Existing socio-psychological studies suggest that users of a social network form their opinions relying on the opinions of their neighbors. According to DeGroot opinion formation model, one value of particular importance is the asymptotic consensus value---the sum of user opinions weighted by the users' eigenvector centralities. This value plays the role of an attractor for the opinions in the network and is a lucrative target for external influence. However, since any potentially malicious control of the opinion distribution in a social network is clearly undesirable, it is important to design methods to prevent the external attempts to strategically change the asymptotic consensus value. In this work, we assume that the adversary wants to maximize the asymptotic consensus value by altering the opinions of some users in a network; we, then, state DIVER---an NP-hard problem of disabling such external influence attempts by strategically adding a limited number of edges to the network. Relying on the theory of Markov chains, we provide perturbation analysis that shows how eigenvector centrality and, hence, DIVER's objective function change in response to an edge's addition to the network. The latter leads to the design of a pseudo-linear-time heuristic for DIVER, whose computation relies on efficient estimation of mean first passage times in a Markov chain. We confirm our theoretical findings in experiments.

Motivation & Objective

• To address the growing threat of adversarial manipulation of opinion dynamics in social networks through strategic user influence.
• To formalize the problem of restoring the original asymptotic consensus value after external manipulation, where only edge addition is allowed as a countermeasure.
• To design a scalable, efficient algorithm that identifies optimal edges to add, minimizing the impact of adversarial opinion shifts.
• To prove the NP-hardness of the problem and develop a practical heuristic grounded in Markov chain theory and eigenvector centrality perturbation.

Proposed method

• Formalizing DIVER as an NP-hard optimization problem to restore the original asymptotic consensus value by adding a limited number of edges.
• Applying perturbation analysis to model how eigenvector centrality changes upon edge addition, enabling estimation of edge impact.
• Defining edge scores based on the potential change in the objective function, using mean first passage times (MFPT) in Markov chains to estimate centrality shifts.
• Designing a greedy, pseudo-linear-time heuristic that selects edges with highest estimated impact, using only top-centrality nodes for efficient computation.
• Implementing iterative edge addition with stopping criteria based on convergence to the original consensus value or maximum edge limit.
• Validating the method via experiments on synthetic networks, comparing exact and estimated edge quality scores and tracking convergence of the asymptotic consensus value.

Experimental results

Research questions

• RQ1 How can a social network counteract adversarial manipulation that increases the asymptotic consensus value through opinion alteration of key users?
• RQ2 What is the computational complexity of restoring the original consensus value via edge addition, and can it be solved efficiently?
• RQ3 How do eigenvector centralities and the asymptotic consensus value change in response to a single edge addition in a directed network?
• RQ4 Can mean first passage times in Markov chains be efficiently estimated to guide edge recommendation in large-scale networks?
• RQ5 To what extent can a heuristic based on approximate centrality estimation preserve the effectiveness of edge recommendation?

Key findings

• DIVER is proven to be NP-hard, even for undirected networks, establishing the computational intractability of the problem.
• The proposed heuristic achieves convergence to within 10% of the original asymptotic consensus value using 180 edges when estimating edge scores with 20% of top-centrality nodes.
• Using exact computation of edge scores, the method restores the consensus value to within 10^-8 of the original state in 17 iterations (85 edges).
• The heuristic performs well even with approximate centrality estimation, selecting mostly high-quality edges despite a small number of suboptimal choices.
• The method scales effectively, achieving pseudo-linear time complexity by leveraging efficient MFPT estimation for high-centrality states.
• Theoretical insights into eigenvector centrality perturbation under edge addition provide a foundation for broader applications in network control and opinion dynamics.