Multilayer networks (Chair: MIKKO KIVELÄ)

Network science provides a powerful framework for modeling complex systems, where the intricate interplay between structure and dynamics often leads to the emergence of complex behaviors such as synchronization and collective motion. Random walks, as one of the most studied stochastic processes, play a central role in exploring this interplay. However, traditional models often assume independent random walkers, overlooking real-world constraints such as finite carrying capacities at nodes. Addressing this limitation, recent studies introduced nonlinear diffusion processes that account for node capacity limits, enabling the inference of network structure through localized measurements and inverse problem-solving. In this work, we extend these nonlinear diffusion models to multigraphs, where nodes are connected by multiple types of links, each carrying distinct attributes. Examples of such systems include air transport networks categorized by airlines or social networks differentiated by interaction platforms. We show how the degree distribution of an entire multigraph can be reconstructed by combining knowledge of one link type with stationary density measurements from a single node. Through simulations on diverse multigraph topologies, including Erdős-Rényi, Watts-Strogatz, and scale-free networks, we evaluate the reconstruction accuracy and robustness of the proposed approach. Our findings demonstrate the capability to accurately infer key structural properties, such as degree distribution and moments, even under varying levels of sparsity and topology. This study strengthens the connection between network dynamics and topology, offering a novel framework for structural inference in multigraphs with limited information.

Due to the widespread digitization of biomedical and behavioral data, there has been a breakthrough in our abil- ity to characterize often overlooked exposome factors in disease, such as social interactions, psychological states, and behavioral patterns such as medical treatments, drug use, drinking habits and diet. This is particularly important to study chronic health conditions which unfold as a complex interplay among biological, psychological, linguistic, and societal multiscale factors that change over time and which traditional organism models cannot capture. The recent availability of heterogeneous multiomics and unconventional data from electronic health records, social media, and digital cohorts, as well as computational and theoretical advances in characterizing multivariate, multilayer complex systems, raise the prospect of “digital twins” in precision medicine, whereby the behavior of a cell, sub-system, organ or a whole organism can be accurately simulated to predict disease and intervention outcomes [1]. Towards that goal, in this presentation we will sum- marize our multilayer network reduction methodology used to uncover multiscale factors in disease (Figure 1). In particular, we show that using distance backbones [2] and effective graphs [3] to remove redundant edges or in- teractions from network models obtained from biochem- ical and social data, reveals optimal information trans- mission and regulatory pathways. This greatly facili- tates explainable inference, which is essential in biomed- ical settings. Indeed, by removing large proportions of redundant associations and interactions, it is feasible to use the remaining ones to directly backtrack to empir- ical evidence, i.e. the data items used to characterize correlational strength or information about causal dy- namics when available. We demonstrate the approach with results from papers published or under review in the last year: [1,4,5,6,7,8]. Finally, we demonstrate that our network reduction approach naturally extends to multilayer networks. This is exemplified with recent studies of multi-organism male infertility from protein interaction networks [9] and patient-centered integration and analysis of heterogeneous data sources in epilepsy, ranging from social media data to electronic health records [10,11

Multilayer networks are an effective tool for studying variability across an ensemble of networks [1-3]. Traditionally, coupling between layers is defined uniformly by a single parameter, but this approach risks mischaracterizing variability that is consequential for brain function. We leverage the richness of the Human Connectome Project dataset, pitting the uniform model against the informed model to predict a suite of outcome measures. For both models, layer l is defined by subject l’s brain network, as indexed by the Pearson correlation of the time series of the 100 region Schaefer parcellation (see Fig 1a). In the uniform model, all-to-all coupling of layers (i.e., inter-brain coupling) is defined traditionally (see Fig 1b). Inter-brain coupling in the informed model is defined by computing the correlation between all subjects across 9 measures of the social environment (see Fig 1c) and using a mixture model that allows us to tune how much social context similarity informs interlayer coupling (see Fig 1d). We use flexibility and community assignments to compare how well these models predict 37 outcome measures. Community structure of the uniform coupling model is dominated by two communities (see Fig 1e). The flexibility of nodes across canonical brain systems varies as expected (see Fig 1f). We found moderate to no predictive power of the uniform model on the outcome measures (see Fig 1g). As inter-brain coupling is increasingly informed by social context similarity, we see greater diversity in community assignments (see Fig 1h), a shift in canonical systems’ flexibility (see Fig 1i), and an improvement on some predictions, e.g. mental health (see Fig 1j). Informed inter-brain coupling in a multilayer model provides useful context for understanding variability in brain network organization. This context serves to improve predictions on associations with mental health outcomes, which has consequences for the identification of brain-network based biomarkers.

Each year, the CDC hosts the FluSight Forecast Challenge, where over 40 teams contribute to the flu forecasts. To create an ensemble forecast, the CDC takes the median of each quantile prediction across all models, assuming each provides statistically independent information. However, this assumption may not always hold, as models may share analytical frameworks, code, data, or calibrate on the same target variables (e.g. flu season peaks). The focus is to isolate sources of independent error and identify clusters of similar models to better understand ensemble performance and limitations.Using methodologies from climate forecasting, we first quantify the “effective number” of independent models by isolating independent noise from predictions. Our findings reveal that the effective number of models providing unique information is around 6—far fewer than the total number of models—indicating significant redundancy in the FluSight ensemble. This emphasizes a significant limitation in the current ensemble approach, where non-independent contributions may inflate the perceived diversity of forecasts.To further explore model dependencies, we apply a multilayer network clustering approach, combining similarity measures and multilayer community detection to cluster models with shared error patterns. Synthetic data experiments validate the pipeline’s robustness, correctly identifying ground truth groupings with independent, group-specific, and correlated noise. When applied to FluSight models, we observe temporal inconsistencies in groupings, likely driven by updates to individual models throughout the flu season.Our results highlight the need to address model interdependencies in epidemic forecasting. By quantifying the effective number of independent models and providing tools to isolate independent error, we offer a framework for improving ensemble reliability. These insights are essential for enhancing forecast accuracy and supporting public health decision-making.

Traditional social network analysis often reduces homophily—the tendency of similar individuals to connect—to a single parameter, neglecting nuanced biases within and across groups. We propose an exponential family model that incorporates both local homophily (strong ties within cliques) and global homophily (weaker ties across communities), using a maximum entropy approach to analyze their effects on network dynamics under percolation. This framework decomposes homophily into finer levels, revealing how these interactions shape the spread of information, diseases, and innovation. Testing on diverse datasets, the model highlights how varying homophily patterns influence percolation thresholds and the effectiveness of interventions, offering valuable insights for public health strategies, social media information flow, and targeted mitigation efforts.