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Piotr Bródka

Publications and source records attributed to Piotr Bródka.

At least 19 recordsLinked to original sources
arXiv2026

Graph Data Augmentation via Contrastive Generator Inversion ($\texttt{DCBA}$)

Graphs provide a natural representation of many complex systems, ranging from social platforms to ecosystems. However, the development of graph-based machine learning methods is often constrained by the limited availability of large and diverse graph datasets. In this paper, we introduce $\texttt{DCBA}$, a model-based approach to graph data augmentation that infers the configuration of a synthetic graph generator from an observed network. We instantiate the proposed framework using the $\texttt{ABCD}$ generator, which produces scale-free networks with community structure. Our model learns a joint representation of graphs and generator parametrisations using a multi-positive contrastive objective with soft negative weighting. The learned representation enables the prediction of an $\texttt{ABCD}$ configuration whose stochastic realisations preserve the macrostructural properties encoded by the generator. Experiments show that $\texttt{DCBA}$ recovers generator parameters more accurately and robustly than an algorithmic inverse-modelling baseline. Its downstream utility is further demonstrated in community detection, where inferred configurations used to fine-tune $\texttt{PRoCD}$ improve AMI on average by $161\%$ on synthetic and $273\%$ on real-world networks.

cs.LG↗
arXiv2026

Graph Reduction in Multirelational Networks: A Spreading-Oriented Reduction Benchmark

Real-world networks are inherently incomplete, noisy, and dynamically evolving, making it difficult to capture all actors and their relationships. Their scale often renders direct analysis computationally demanding. While influence maximisation (IM) has been widely studied, the role of graph reduction as a preprocessing step, and its impact on IM accuracy, remains underexplored. In this work, we introduce the Spreading-Oriented Reduction Benchmark (SORB), an open-source, standardised framework for systematically evaluating IM models across diverse task settings. SORB provides an extensible pipeline operating on a representative collection of real-world networks, including single- and multilayer structures, and accounts for graph reduction directly into the evaluation process. This design shifts the focus from analysing IM algorithms in isolation to quantifying how graph reduction alters predictive performance. Using SORB, we study the effects of sparsification and coarsening across multiple IM scenarios. Our results show that the impact of reduction is strongly dependent on both the network type (single-layer vs. multirelational) and the downstream task ($Gain@k$ vs. $\mathrm{AUC}_{\mathrm{cutoff}}$): sparsification preserves seed set quality on single-layer networks, whereas flattened multilayer networks exhibit systematic ranking degradation regardless of reduction strategy. These findings highlight the importance of reduction-aware, multi-task evaluation when studying spreading processes in complex networks.

cs.SI↗
arXiv2026

Towards Graph Foundation Models for Dynamics in Complex Networked Systems: Lessons from Super-Spreader Identification in Multilayer Networks

Network dynamics - including spreading, influence maximisation, and epidemic modelling - remain largely confined to the transductive paradigm, where models are trained on a single network and cannot be reused on unseen graphs without retraining. We argue that inductive cross-network generalisation is a necessary prerequisite for Graph Foundation Models (GFMs) in this domain and propose four design properties towards this goal. As a proof of concept, ts-net (TopSpreadersNetwork), trained solely on synthetic multilayer networks (MLNs), demonstrates zero-shot generalisation to real-world MLNs of varying size and layer count, outperforming classical heuristics and transductive baselines on three of four metrics. Based on ts-net's performance, we further outline five open challenges towards building GFMs for network dynamics: scale, many-layer generalisation, self-supervised pretraining, cross-task transfer, and node-attribute integration.

cs.LG↗
arXiv2026

The Elusive Nature of Roughness: Linking Hydraulics and Graph Theory for Water Distribution Networks Model Calibration

Accurate pipe roughness estimation in large-scale water distribution networks is often hindered by the high cost of traditional field methods. This study investigates whether network partitioning, by utilizing hydraulic and graph-derived attributes, can enhance the calibration of these parameters. Using a high-fidelity model of a real network as a benchmark, we evaluate density-based clustering, and topology-driven grouping strategies. Optimization experiments demonstrate that attribute-based grouping yields stable, repeatable results comparable to manual calibration for hydraulically significant pipes. While hydraulic attributes generate more distinct cluster structures, the inclusion of graph-based data improves calibration robustness by stabilizing the optimization process. Notably, density-based clustering achieves similar accuracy to k-means while reducing computational effort in specific configurations. Although the method does not eliminate all sources of uncertainty, results suggest that topology-informed grouping provides a systematic, reproducible, and computationally efficient alternative to manual heuristics, highlighting the critical role of network structure in reliable parameter estimation.

cs.CE↗
arXiv2026

Twinning Complex Networked Systems: Data-Driven Calibration of the mABCD Synthetic Graph Generator

The increasing availability of relational data has contributed to a growing reliance on network-based representations of complex systems. Over time, these models have evolved to capture more nuanced properties, such as the heterogeneity of relationships, leading to the concept of multilayer networks. However, the analysis and evaluation of methods for these structures is often hindered by the limited availability of large-scale empirical data. As a result, graph generators are commonly used as a workaround, albeit at the cost of introducing systematic biases. In this paper, we address the inverse-generator problem by inferring the configuration parameters of a multilayer network generator, \mABCD, from a real-world system. Our goal is to identify parameter settings that enable the generator to produce synthetic networks that act as digital twins of the original structure. We propose a method for estimating matching configurations and for quantifying the associated error. Our results demonstrate that this task is non-trivial, as strong interdependencies between configuration parameters weaken independent estimation and instead favour a joint-prediction approach.

cs.SI↗
arXiv2026

Beyond Individual Influence: The Role of Echo Chambers and Community Seeding in the Multilayer three state q-Voter Model

The diffusion of complex opinions is severely hindered in multilayer social networks by echo chambers and cognitive consistency mechanisms. We investigate Influence Maximization strategies within the 3-state multilayer q-voter model. Utilizing the mABCD benchmark, we simulate social environments ranging from integrated Open Worlds to segregated Fortress Worlds. Our results reveal a topological paradox that we term the "Fortress Trap". In highly modular networks, strategies maximizing local density such as Clique Influence Maximization (CIM) and k-Shell fail to trigger global cascades, creating isolated bunkers of consensus due to the Overkill Effect. Furthermore, we identify a Redundancy Trap in perfectly aligned Clan topologies, where the structural overlap of layers creates a "Perfect Prison," rendering it the most resistant environment to diffusion. We demonstrate that VoteRank, a strategy that prioritizes diversity of reach over local intensity, consistently outperforms structure-based methods. These findings suggest that, for complex contagion, maximizing topological entropy is more effective than reinforcing local clusters.

cs.SI↗
arXiv2025

Multilayer Artificial Benchmark for Community Detection (mABCD)

One of the most persistent challenges in network science is the development of various synthetic graph models to support subsequent analyses. Among the most notable frameworks addressing this issue is the Artificial Benchmark for Community Detection (ABCD) model, a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs similar to the well-known LFR model but it is faster, more interpretable, and can be investigated analytically. In this paper, we use the underlying ingredients of ABCD and introduce its variant, mABCD, thereby addressing the gap in models capable of generating multilayer networks. The uniqueness of the proposed approach lies in its flexibility at both levels of modelling: the internal structure of individual layers and the inter-layer dependencies, which together make the network a coherent structure rather than a collection of loosely coupled graphs. In addition to the conceptual description of the framework, we provide a comprehensive analysis of its efficient Julia implementation. Finally, we illustrate the applicability of mABCD to one of the most prominent problems in the area of complex systems: spreading phenomena analysis.

cs.SI↗
arXiv2025

Applicability of the Minimal Dominating Set for Influence Maximization in Multilayer Networks

The minimal dominating set (MDS) is a well-established concept in network controllability and has been successfully applied in various domains, including sensor placement, network resilience, and epidemic containment. In this study, we adapt the local-improvement MDS routine and explore its potential for enhancing seed selection for influence maximization in multilayer networks (MLN). We employ the Linear Threshold Model (LTM), which offers an intuitive representation of influence spread or opinion dynamics by accounting for peer influence accumulation. To ensure interpretability, we utilize rank-refining seed selection methods, with the results further filtered with MDS. Our findings reveal that incorporating MDS into the seed selection process improves spread only within a specific range of situations. Notably, the improvement is observed for larger seed set budgets, lower activation thresholds, and when an "AND" strategy is used to aggregate influence across network layers. This scenario reflects situations where an individual does not require the majority of their acquaintances to hold a target opinion, but must be influenced across all social circles.

cs.SI↗
arXiv2025

Identifying Super Spreaders in Multilayer Networks

Identifying super-spreaders can be framed as a subtask of the influence maximisation problem. It seeks to pinpoint agents within a network that, if selected as single diffusion seeds, disseminate information most effectively. Multilayer networks, a specific class of heterogeneous graphs, can capture diverse types of interactions (e.g., physical-virtual or professional-social), and thus offer a more accurate representation of complex relational structures. In this work, we introduce a novel approach to identifying super-spreaders in such networks by leveraging graph neural networks. To this end, we construct a dataset by simulating information diffusion across hundreds of networks - to the best of our knowledge, the first of its kind tailored specifically to multilayer networks. We further formulate the task as a variation of the ranking prediction problem based on a four-dimensional vector that quantifies each agent's spreading potential: (i) the number of activations; (ii) the duration of the diffusion process; (iii) the peak number of activations; and (iv) the simulation step at which this peak occurs. Our model, TopSpreadersNetwork, comprises a relationship-agnostic encoder and a custom aggregation layer. This design enables generalisation to previously unseen data and adapts to varying graph sizes. In an extensive evaluation, we compare our model against classic centrality-based heuristics and competitive deep learning methods. The results, obtained across a broad spectrum of real-world and synthetic multilayer networks, demonstrate that TopSpreadersNetwork achieves superior performance in identifying high-impact nodes, while also offering improved interpretability through its structured output.

cs.SI↗
arXiv2025

Rank-Refining Seed Selection Methods for Budget Constrained Influence Maximisation in Multilayer Networks under Linear Threshold Model

The problem of selecting an optimal seed set to maximise influence in networks has been a subject of intense research in recent years. However, despite numerous works addressing this area, it remains a topic that requires further elaboration. Most often, it is considered within the scope of classically defined graphs with a spreading model in the form of Independent Cascades. In this work, we focus on the problem of budget-constrained influence maximisation in multilayer networks using a Linear Threshold Model. Both the graph model and the spreading process we employ are less prevalent in the literature, even though their application allows for a more precise representation of the opinion dynamics in social networks. This paper aims to answer which of the sixteen evaluated seed selection methods is the most effective and how similar they are. Additionally, we focus our analysis on the impact of spreading model parameters, network characteristics, a budget, and the seed selection methods on the diffusion effectiveness in multilayer networks. Our contribution also includes extending several centrality measures and heuristics to the case of such graphs. The results indicate that all the factors mentioned above collectively contribute to the effectiveness of influence maximisation. Moreover, there is no seed selection method which always provides the best results. However, the seeds chosen with VoteRank-based methods (especially with the $v-rnk-m$ variant we propose) usually provide the most extensive diffusion.

cs.SI↗
arXiv2024

Identifying Key Nodes for the Influence Spread using a Machine Learning Approach

The identification of key nodes in complex networks is an important topic in many network science areas. It is vital to a variety of real-world applications, including viral marketing, epidemic spreading and influence maximization. In recent years, machine learning algorithms have proven to outperform the conventional, centrality-based methods in accuracy and consistency, but this approach still requires further refinement. What information about the influencers can be extracted from the network? How can we precisely obtain the labels required for training? Can these models generalize well? In this paper, we answer these questions by presenting an enhanced machine learning-based framework for the influence spread problem. We focus on identifying key nodes for the Independent Cascade model, which is a popular reference method. Our main contribution is an improved process of obtaining the labels required for training by introducing 'Smart Bins' and proving their advantage over known methods. Next, we show that our methodology allows ML models to not only predict the influence of a given node, but to also determine other characteristics of the spreading process-which is another novelty to the relevant literature. Finally, we extensively test our framework and its ability to generalize beyond complex networks of different types and sizes, gaining important insight into the properties of these methods.

cs.SI↗
arXiv2024

Network Diffusion -- Framework to Simulate Spreading Processes in Complex Networks

With the advancement of computational network science, its research scope has significantly expanded beyond static graphs to encompass more complex structures. The introduction of streaming, temporal, multilayer, and hypernetwork approaches has brought new possibilities and imposed additional requirements. For instance, by utilising these advancements, one can model structures such as social networks in a much more refined manner, which is particularly relevant in simulations of the spreading processes. Unfortunately, the pace of advancement is often too rapid for existing computational packages to keep up with the functionality updates. This results in a significant proliferation of tools used by researchers and, consequently, a lack of a universally accepted technological stack that would standardise experimental methods (as seen, e.g. in machine learning). This article addresses that issue by presenting an extended version of the Network Diffusion library. First, a survey of the existing approaches and toolkits for simulating spreading phenomena is shown and then, an overview of the framework functionalities. Finally, we report four case studies conducted with the package to demonstrate its usefulness: the impact of sanitary measures on the spread of COVID-19, the comparison of information diffusion on two temporal network models, and the effectiveness of seed selection methods in the task of influence maximisation in multilayer networks. We conclude the paper with a critical assessment of the library and the outline of still awaiting challenges to standardise research environments in computational network science.

cs.SI↗
arXiv2024

The role of conformity in opinion dynamics modelling with multiple social circles

Interaction with others influences our opinions and behaviours. Our activities within various social circles lead to different opinions expressed in various situations, groups, and ways of communication. Earlier studies on agent-based modelling of conformism within networks were based on a single-layer approach. Contrary to that, in this work, we propose a model incorporating conformism in which a person can share different continuous opinions on different layers depending on the social circle. Afterwards, we extend the model with more components that are known to influence opinions, e.g. authority or openness to new views. These two models are then compared to show that only sole conformism leads to opinion convergence.

cs.SI↗
arXiv2023

Influence of Information Blocking on the Spread of Virus in Multilayer Networks

In this paper, we present the model of the interaction between the spread of disease and the spread of information about the disease in multilayer networks. Next, based on the characteristics of the SARS-COV-2 virus pandemic, we evaluated the influence of information blocking on the virus spread. Our results show that blocking the spread of information affects the speed at which the epidemic peak appears in our society and the number of infected individuals.

cs.SI↗
arXiv2022

Maximising Influence Spread in Complex Networks by Utilising Community-based Driver Nodes as Seeds

Finding a small subset of influential nodes to maximise influence spread in a complex network is an active area of research. Different methods have been proposed in the past to identify a set of seed nodes that can help achieve a faster spread of influence in the network. This paper combines driver node selection methods from the field of network control, with the divide-and-conquer approach of using community structure to guide the selection of candidate seed nodes from the driver nodes of the communities. The use of driver nodes in communities as seed nodes is a comparatively new idea. We identify communities of synthetic (i.e., Random, Small-World and Scale-Free) networks as well as twenty-two real-world social networks. Driver nodes from those communities are then ranked according to a range of common centrality measures. We compare the influence spreading power of these seed sets to the results of selecting driver nodes at a global level. We show that in both synthetic and real networks, exploiting community structure enhances the power of the resulting seed sets.

cs.SI↗
arXiv2022

Modeling the impact of external influence on green behaviour spreading in multilayer financial networks

Growing awareness of the impact of business activity on the environment increases the pressure on governing bodies to address this issue. One possibility is to encourage or force the market into green behaviours. However, it is often hard to predict how different actions affect the market. Thus, to help with that, in this paper, we have proposed the green behaviour spreading model in the bank-company multilayer network. This model allows assessing how various elements like the duration of external influence, targeted market segment, or intensity of action affect the outcome regarding market greening level. The model evaluation results indicate that governing bodies, depending on the market "openness" to green activities, can adjust the duration and intensity of the proposed action. The strength of the impact can be changed by the public or private authority with the use of obligatory or voluntary rules and the proportion of influenced banks. This research may be helpful in the process of creating the optimal setups and increasing the performance of greening policies implementation.

cs.SI↗
arXiv2022

Simulating Spreading of Multiple Interacting Processes in Complex Networks

Investigating the interaction between spreading processes in complex networks is one of the most important challenges in network science. However, whether we would like to know how the information campaign will affect virus spreading or how the advertising campaign of the new iPhone will affect the sales of Samsung phones, we need an environment that will allow us to evaluate under what conditions our spreading campaign will be effective. Network Diffusion is a Python package that should help do that. In this paper, we introduce its operating principle and main functionalities, including simple examples of simulations that can be performed using it.

cs.SI↗