Dynamics 3 (Chair: MICHELE COSCIA)
Matrix-weighted networks for modeling multidimensional dynamics
Presenter: Yu Tian
Time: Thu 16:30 - 16:45
Authors: Yu Tian (Max Planck Institute for Physics of Complex Systems | Cell Biology and Genetics)*; Sadamori Kojaku (Binghamton University); Hiroki Sayama (Binghamton University, State University of New York); Renaud Lambiotte (University of Oxford)
Abstract
Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions.For example, in social networks, individuals often have multiple interconnected opinions that can affect different opinions of other individuals, which can be better characterized by matrices.We propose a novel, general framework for modeling such multidimensional interacting dynamics: matrix-weighted networks (MWNs). We present the mathematical foundations of MWNs and examine consensus dynamics and random walks within this context. Our results reveal that the coherence of MWNs gives rise to non-trivial steady states that generalize the notions of communities and structural balance in traditional networks.
Co-evolving Networks for Opinion and Social Dynamics in Agent-Based Models
Presenter: Natasa Djurdjevac Conrad
Time: Thu 16:45 - 17:00
Authors: Natasa Djurdjevac Conrad (Zuse Institute Berlin)*; Nhu Quang Vu (Freie Universitaet Berlin); Soeren Nagel (Zuse Institute Berlin )
Abstract
Digital media has fundamentally transformed social interactions and reshaped the ways in which individual opinions influence and are influenced by these interactions [2]. While many studies explore how opinions influence social ties, existing models mostly fail to include the interplay between opinion and social dynamics. We introduce a novel stochastic agent-based model (ABM) [1] that captures this co-evolutionary process. Our model considers agents moving in a social space influenced by both positions and opinions of other agents. Agents with similar opinions of the same stance exhibit social closeness, while opinion dissimilarity reinforces social distancing between agents. Opinion dynamics is driven by agents’ spatial proximity and their opinion similarity. By analyzing the underlying social and opinion temporal interaction networks, we explore the emergence of phenomena like echo chambers and opinion consensus [3]. We apply our model to General Social Survey Data (GSS) [4], demonstrating its ability to capture the co-evolution of political identity and individual opinions regarding governmental issues, see Figure. Our findings highlight the crucial role of this interplay in shaping social structures and collective outcomes.
Rumor propagation on hypergraphs
Presenter: Pietro Traversa
Time: Thu 17:00 - 17:15
Authors: Kleber Oliveira (Munster Technological University)*; Pietro Traversa (CENTAI Institute); Guilherme Ferraz de Arruda (CENTAI Institute); Yamir Moreno (Universidad de Zaragoza)
Abstract
While much of research done on rumor and information propagation focuses on settings which are adequately described by traditional dyadic networks, namely micro-blogging social media, an increasing amount of communication in populous countries such as Brazil, India and Indonesia is exchanged via messenger mobile apps (such as Whatsapp and Telegram), which elude the simple network description since messages travel from group to group.To address this gap, we propose a rumor propagation model on hypergraphs suited to higher-order dynamics. Our model has three possible node states, ignorant (X), spreader (Y) and stifler (Z). An ignorant node becomes a spreader (contagion) with rate λ once one of its groups reached a critical mass of spreaders (defined with a threshold θ_λ), a mechanism introduced before in related work. However, here we also keep track of how many groups reached the critical mass thus becoming active. Then, a spreader becomes a stifler (annihilation) with rate α once enough of their groups are active, which is controlled with a threshold θ_α.We conduct computational experiments to investigate the parameter space of the model and find that it reveals a rich variety of behaviors, with regions in the parameter space capable of exhibiting both spontaneous recovery (where the absorbing time τ decays exponentially) and group-mediated recovery (τ decays as a power-law of the contagion rate λ), depending on each node hyperdegree. The latter is seen on typical rumor propagation dynamics in the literature.Furthermore, we extend the study of the mechanisms proposed in our model by looking into two empirical datasets (Telegram, email-Eu). Considering aggregated statistics of interevent time and duration of information cascades, we compare simulations of our model on the empirical hypergraphs with the statistics from timestamps in the datasets and show that the parametric space is capable of capturing some of the temporal dynamics in the real-world systems.
Stationary distribution of node2vec random walks on household models
Presenter: Lars Schroeder
Time: Thu 17:15 - 17:30
Authors: Lars Schroeder (University of Twente)*; Clara Stegehuis (University of Twente)
Abstract
node2vec random walks are tuneable random walks that come from the popular algorithm node2vec which is used for network embedding. The transition prob`abilities of the random walks depend on the previous visited node and on the triangles that contain the current and the previous node. In the node2vec algorithm, node2vec random walks are used to sample neighborhoods for each node of the network and by comparing these an embedding of the network into a Euclidean space can be computed. Since the parameters of the random walks can be tuned to create different types of neighborhoods, this approach is very flexible and advantageous over just using simple random walks.Even though the algorithm is widely used in practice, mathematical properties of node2vec random walks almost have not been investigated and even basic questions such as how the stationary distribution depends on the walk parameters are unexplored. We study household models, graphs with clique-structured communities, and we present an explicit formula for the stationary distribution of node2vec random walks on these models and compare it with the stationary distribution of the simple random walk. The stationary distribution varies strongly depending on the chosen parameters. Since the transition probabilities are only determined by the ratio of $\alpha, \beta$ and $\gamma$, we can fix $\gamma = 1$. Comparing the other two parameters, changing $\beta$ seems to have a much stronger effect than changing $\alpha$. The larger $\beta$ is chosen, the longer the random walk stays in bigger cliques which leads to higher stationary probabilities of the nodes of that cliques. Numerical results show that for $\alpha \to \infty$ the node2vec and the simple random walk converge to the same stationary distribution.
Modeling opinion dynamics of LLM populations
Presenter: Erica Cau
Time: Thu 17:30 - 17:45
Authors: Erica Cau (University of Pisa)*; Valentina Pansanella (ISTI-CNR); Giulio Rossetti (ISTI-CNR)
Abstract
As inherently social beings, humans possess the ability to form opinions based on their beliefs and communicate them with others. Opinion evolution in recent decades has been studied in the field of computational social sciences by creating agent-based models (ABMs) interacting and changing opinions according to different criteria. Despite the wide range of insights obtained, these models still suffer from limitations inherent to the mathematical approach, while recent approaches have included Large Language Models (LLMs) to overcome these issues. This preliminary work proposes a framework for allowing complex simulations with LLM agents. The framework builds upon ABMs, where a network connects agents interacting through multiple rounds of discussion. Each agent holds an opinion on a given input statement, quantified on a Likert scale ranging from 0 (strongly disagree) to 6 (strongly agree). Agents engaging in a discussion can be randomly chosen or decided according to an opinion dynamics algorithm. First tests with the framework were conducted in a mean-field scenario with 140 agents having different starting opinion distributions. Experiments leveraged Mistral-7B and Llama3 to simulate discussions on the Theseus’ Ship paradox, a thought experiment that forced agents into well-reasoned discussions, reducing the LLMs bias toward scientific truth. Preliminary results confirm the bias toward approval and excessive politeness by Mistral agents. On the other hand, Llama agents demonstrated instead to accept any opinion, with differences related to the scenario. Especially with a majority of negative opinions, agents tend to be more biased toward the negative side without reaching a positive stance. Moreover, Llama agents were mostly persuaded by fallacious statements (79% of cases), particularly in a polarized context.