Link prediction algorithms for multilayer networks are in principle required to effectively account for the entire layered structure while capturing the unique contexts offered by each layer. However, many existing approaches excel at predicting specific links in certain layers but struggle with others, as they fail to effectively leverage the diverse information encoded across different network layers. In this paper, we present MoE-ML-LP , the first Mixture-of-Experts (MoE) framework specifically designed for multilayer link prediction. Building on top of multilayer heuristics for link prediction, MoE-ML-LP synthesizes the decisions taken by diverse experts, resulting in significantly enhanced predictive capabilities. Our extensive experimental evaluation on real-world and synthetic networks demonstrates that MoE-ML-LP consistently outperforms several baselines and competing methods, achieving remarkable improvements of +60% in Mean Reciprocal Rank, +82% in Hits@1, +55% in Hits@5, and +41% in Hits@10. Furthermore, MoE-ML-LP features a modular architecture that enables the seamless integration of newly developed experts without necessitating the re-training of the entire framework, fostering efficiency and scalability to new experts, paving the way for future advancements in link prediction.

Signed networks represent interactions among users (nodes), with edges labeled as positive for friendly relations and negative for antagonistic ones. The 2-Polarized-Communities ( 2pc ) combinatorial optimization problem seeks two disjoint polarized communities in a signed network, so as to satisfy three conditions: most edges within each community are positive, most edges between communities are negative, and the number of edges satisfying these conditions is high compared to the number of nodes in the communities. The Densest Subgraph ( ds ) problem in unsigned networks consists in finding a subgraph that exhibits maximum ratio between number of edges and number of nodes. Although the 2pc problem intuitively suggests finding a dense subgraph, no prior work has explored the implicitly optimized density measure or algorithmic methods from the rich, yet distinct, literature on the ds problem (in unsigned networks) and applied them to 2pc . This work bridges this gap by formally establishing a link between the two problems and introducing a highly efficient and effective greedy algorithm inspired by ds methods to solve 2pc . Experimental results on synthetic and real datasets demonstrate the superior performance of our method compared to competing approaches in terms of both accuracy and efficiency.

Link prediction has traditionally been studied in the context of simple graphs, although real-world networks are inherently complex as they are often comprised of multiple interconnected components, or layers. Predicting links in such network systems, or multilayer networks, require to consider both the internal structure of a target layer as well as the structure of the other layers in a network, in addition to layer-specific node-attributes when available. This problem poses several challenges, even for graph neural network based approaches despite their successful and wide application to a variety of graph learning problems. In this work, we aim to fill a lack of multilayer graph representation learning methods designed for link prediction. Our proposal is a novel neural-network-based learning framework for link prediction on (attributed) multilayer networks, whose key idea is to combine (i) pairwise similarities of multilayer node embeddings learned by a graph neural network model, and (ii) structural features learned from both within-layer and across-layer link information based on overlapping multilayer neighborhoods. Extensive experimental results have shown that our framework consistently outperforms both single-layer and multilayer methods for link prediction on popular real-world multilayer networks, with an average percentage increase in AUC up to 38%. We make source code and evaluation data available at https://mlnteam-unical.github.io/resources/.

Abstract Given a graph whose edges are assigned positive-type and negative-type weights, the problem of correlation clustering aims at grouping the graph vertices so as to minimize (resp. maximize) the sum of negative-type (resp. positive-type) intra-cluster weights plus the sum of positive-type (resp. negative-type) inter-cluster weights. In correlation clustering, it is typically assumed that the weights are readily available. This is a rather strong hypothesis, which is unrealistic in several scenarios. To overcome this limitation, in this work we focus on the setting where edge weights of a correlation-clustering instance are unknown, and they have to be estimated in multiple rounds, while performing the clustering. The clustering solutions produced in the various rounds provide a feedback to properly adjust the weight estimates, and the goal is to maximize the cumulative quality of the clusterings. We tackle this problem by resorting to the reinforcement-learning paradigm, and, specifically, we design for the first time a Combinatorial Multi-Armed Bandit (CMAB) framework for correlation clustering. We provide a variety of contributions, namely (1) formulations of the minimization and maximization variants of correlation clustering in a CMAB setting; (2) adaptation of well-established CMAB algorithms to the correlation-clustering context; (3) regret analyses to theoretically bound the accuracy of these algorithms; (4) design of further (heuristic) algorithms to have the probability constraint satisfied at every round (key condition to soundly adopt efficient yet effective algorithms for correlation clustering as CMAB oracles); (5) extensive experimental comparison among a variety of both CMAB and non-CMAB approaches for correlation clustering.

We study two novel clustering problems in which the pairwise interactions between entities are characterized by probability distributions and conditioned by external factors within the environment where the entities interact. This covers any scenario where a set of actions can alter the entities' interaction behavior. In particular, we consider the case where the interaction conditioning factors can be modeled as cluster memberships of entities in a graph and the goal is to partition a set of entities such as to maximize the overall vertex interactions or, equivalently, minimize the loss of interactions in the graph. We show that both problems are NP-hard and they are equivalent in terms of optimality. However, we focus on the minimization formulation as it enables the possibility of devising both practical and efficient approximation algorithms and heuristics. Experimental evaluation of our algorithms, on both synthetic and real network datasets, has shown evidence of their meaningfulness as well as superiority with respect to competing methods, both in terms of effectiveness and efficiency.

Community detection and evolution has been largely studied in the last few years, especially for network systems that are inherently dynamic and undergo different types of changes in their structure and organization in communities. Because of the inherent uncertainty and dynamicity in such network systems, we argue that temporal community detection problems can profitably be solved under a particular class of multi-armed bandit problems, namely combinatorial multi-armed bandit (CMAB). More specifically, we propose a CMAB-based methodology for the novel problem of dynamic consensus community detection, i.e., to compute a single community structure that is designed to encompass the whole information available in the sequence of observed temporal snapshots of a network in order to be representative of the knowledge available from community structures at the different time steps. Unlike existing approaches, our key idea is to produce a dynamic consensus solution for a temporal network to have unique capability of embedding both long-term changes in the community formation and newly observed community structures.