Background
Social networks play a central role in shaping how opinions form, spread, and evolve. To study phenomena such as consensus, where individuals eventually agree, and polarization, where the network separates into groups with opposing opinions, researchers often rely on mathematical models, since directly analyzing and controlling opinion dynamics in real-world social systems is challenging. Within this framework, understanding and steering collective outcomes, such as consensus and polarization, has become a fundamental problem in computational social science. Common intervention strategies include modifying the underlying network structure, for example, by adding or removing edges, or altering opinions directly, for example, by changing the initial opinions of selected nodes to promote a desired outcome.
Consider a social network of N individuals, represented by nodes, where edges represent social ties such as friendships. Each node holds a continuous opinion on a given topic. Nodes become active randomly over time and interact with their neighbors. When a node is active, it preferentially selects neighbors with similar opinions, interacts with them, and updates its opinion according to a specified update rule. Interactions may also be reciprocal: the selected neighbor may update its opinion as well, with some fixed probability. Together, these mechanisms define a temporal, homophily-driven model of opinion dynamics.
The system exhibits a critical threshold, determined by the model parameters. Below this threshold, consensus is stable; above it, polarization can emerge. Importantly, the threshold also depends on the underlying network through the spectral radius of an asymmetric weight matrix derived from the graph structure.
This naturally leads to the following network intervention problem. Given a budget of k edge modifications, which missing edges should be added, or which existing edges should be removed, in order to increase or decrease the network’s robustness to polarization? Since the critical threshold quantifies this robustness, the objective is to choose edge modifications that maximize or minimize the threshold.
Tasks
The project consists of the following three tasks.
- Simulation. Implement the opinion dynamics model on synthetic graphs and real-world social networks, such as Reddit, Twitter/X, or Facebook networks. We will first run simulations to study how consensus and polarization emerge under different parameter settings. We will then estimate the empirical critical threshold and compare it with the theoretical threshold predicted by the model.
- Edge surgery via spectral perturbation. For candidate edge additions or removals, estimate the resulting change in the critical threshold using spectral perturbation theory. Since the threshold depends on the spectral radius of an asymmetric weight matrix, adding or removing an edge perturbs the spectrum of this matrix and can therefore shift the critical threshold. We will compute these spectral changes efficiently and use them to select the best k edge modifications under a given budget. We will compare the resulting greedy strategy with simple baselines, including random edge selection and centrality-based heuristics, such as adding edges between high-degree nodes or between nodes with large opinion differences.
- Optimization. Formulate the intervention problem as selecting a set S of at most k edge modifications to maximize or minimize the change in robustness to polarization, denoted by f(S). We will then develop algorithms, ideally with theoretical guarantees, for solving this optimization problem. This task provides a principled bridge between the empirical simulations and a theoretically grounded framework for network intervention.
Requirements
Strong foundation in algorithms, linear algebra, graph theory, and machine learning, plus basic experience with Python and libraries such as NetworkX and NetworKit.
Related References
- Modeling echo chambers and polarization dynamics in social networks, Physical Review Letters, 2020.
- Minimizing Polarization and Disagreement in Social Networks, WWW 2018.
Contact
Supervisor: Ahad N. Zehmakan
Email: ahadn.zehmakan@anu.edu.au.com
If you are interested, please write me an email, including (1) what aspects of this project interest you the most, (2) what type of research project you are looking for, 6-unit, 12-unit, or 24-unit, (3) a copy of your transcripts and/or CV, (4) any questions you may have.