This paper presents the Greedy Min-Cut Bayesian Consensus (GMCBC) algorithm for the structural fusion of Bayesian Networks (BNs). The method is designed to preserve essential dependencies while controlling network complexity. It addresses the limitations of traditional fusion approaches, which often lead to excessively complex models that are impractical for inference, reasoning, or real-world applications. As the number and size of input networks increase, this issue becomes even more pronounced. GMCBC integrates principles from flow network theory into BN fusion, adapting the Backward Equivalence Search (BES) phase of the Greedy Equivalence Search (GES) algorithm and applying the Ford-Fulkerson algorithm for minimum cut analysis. This approach removes non-essential edges, ensuring that the fused network retains key dependencies while minimizing unnecessary complexity. Experimental results on synthetic Bayesian Networks demonstrate that GMCBC achieves near-optimal network structures. In federated learning simulations, GMCBC produces a consensus network that improves structural accuracy and dependency preservation compared to the average of the input networks, resulting in a structure that better captures the real underlying (in)dependence relationships. This consensus network also maintains a similar size to the original networks, unlike unrestricted fusion methods, where network size grows exponentially.

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks -- neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. Neural networks are well-established for predicting, generating, and transforming data. A newer paradigm is to treat the parameters of neural networks themselves as data. This insight inspired researchers to suggest neural architectures that can predict properties of trained neural networks (Eilertsen et al., 2020), generate new networks (Erkoç et al., 2023), optimize networks (Metz et al., 2022), or otherwise transform them (Navon et al., 2023; Zhou et al., 2023a). We refer to these neural networks that process other neural networks as metanetworks, or metanets for short. Metanets enable new applications, but designing them is nontrivial. A common approach is to flatten the network parameters into a vector representation, neglecting the input network structure. More generally, a prominent challenge in metanet design is that the space of neural network parameters exhibits symmetries. For example, permuting the neurons in the hidden layers of a Multilayer Perceptron (MLP) leaves the network output unchanged (Hecht-Nielsen, 1990). Instead, equivariant metanets respect these symmetries, so that if the input network is permuted then the metanet output is permuted in the same way. Recently, several works have proposed equivariant metanets that have shown significantly improved performance (Navon et al., 2023; Zhou et al., 2023a;b). However, these networks typically require highly specialized, hand-designed layers that can be difficult to devise.

This paper presents a new decision support system offered for an in-depth analysis of semantic networks, which can provide insights for a better exploration of a brand's image and the improvement of its connectivity. In terms of network analysis, we show that this goal is achieved by solving an extended version of the Maximum Betweenness Improvement problem, which includes the possibility of considering adversarial nodes, constrained budgets, and weighted networks - where connectivity improvement can be obtained by adding links or increasing the weight of existing connections. We present this new system together with two case studies, also discussing its performance. Our tool and approach are useful both for network scholars and for supporting the strategic decision-making processes of marketing and communication managers.

--Clustering is a crucial component of many data mining systems involving the analysis and exploration of various data. Data diversity calls for clustering algorithms to be accurate while providing stable (i.e., deterministic and robust) results on arbitrary input networks. Moreover, modern systems often operate with large datasets, which implicitly constrains the complexity of the clustering algorithm. Existing clustering techniques are only partially stable, however, as they guarantee either determinism or robustness. T o address this issue, we introduce DAOC, a Deterministic and Agglomerative Overlapping Clustering algorithm. DAOC leverages a new technique called Overlap Decomposition to identify fine-grained clusters in a deterministic way capturing multiple optima. In addition, it leverages a novel consensus approach, Mutual Maximal Gain, to ensure robustness and further improve the stability of the results while still being capable of identifying micro-scale clusters. Our empirical results on both synthetic and real-world networks show that DAOC yields stable clusters while being on average 25% more accurate than state-of-the-art deterministic algorithms without requiring any tuning. Our approach has the ambition to greatly simplify and speed up data analysis tasks involving iterative processing (need for determinism) as well as data fluctuations (need for robustness) and to provide accurate and reproducible results. Clustering is a fundamental part of data mining with a wide applicability to statistical analysis and exploration of physical, social, biological and informational systems.

Abstract--The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their advantages inanalyzing large-scale networks. However, most existing NRL methods are designed to preserve the local topology of a network, they fail to capture the global topology. To tackle this issue, we propose a new NRL framework, named HSRL, to help existing NRL methods capture both the local and global topological information of a network. Then, an existing NRL method is used to learn node embeddings for each compressed network. Finally, the node embeddings of the input network are obtained by concatenating the node embeddings from all compressed networks. Empirical studies for link prediction on five real-world datasets demonstrate the advantages of HSRL over state-of-the-art methods. I. INTRODUCTION The science of networks has been widely used to understand thebehaviours of complex systems.

Relational classification has been extensively studied recently due to its applications in social, biological, technological, and information networks. Much of the work in relational learning has focused on analyzing input data that comprise a single network. Although machine learning researchers have considered the issue of how to sample training and test sets from the input network (for evaluation), the mechanisms which are used to construct the input networks have largely been ignored. In most cases, the input network has itself been sampled from a larger target network (e.g., Facebook) and often the researcher is unaware of how the input network was constructed or what impact that may have on evaluation of the relational models. Since the goal in evaluating relational classification algorithms is to accurately assess their performance on the larger target network, it is critical to understand what impact the initial sampling method may have on our estimates of classification accuracy.In this paper, we present different sampling methods and systematically study their impact on evaluation of relational classification. Our results indicate that the choice of sampling method can impact classification performance, and thus consequently affects the accuracy of evaluation.