Multimodal recommender systems (RSs) represent items in the catalog through multimodal data (e.g., product images and descriptions) that, in some cases, might be noisy or (even worse) missing. In those scenarios, the common practice is to drop items with missing modalities and train the multimodal RSs on a subsample of the original dataset. To date, the problem of missing modalities in multimodal recommendation has still received limited attention in the literature, lacking a precise formalisation as done with missing information in traditional machine learning. In this work, we first provide a problem formalisation for missing modalities in multimodal recommendation. Second, by leveraging the user-item graph structure, we re-cast the problem of missing multimodal information as a problem of graph features interpolation on the item-item co-purchase graph. On this basis, we propose four training-free approaches that propagate the available multimodal features throughout the item-item graph to impute the missing features. Extensive experiments on popular multimodal recommendation datasets demonstrate that our solutions can be seamlessly plugged into any existing multimodal RS and benchmarking framework while still preserving (or even widen) the performance gap between multimodal and traditional RSs. Moreover, we show that our graph-based techniques can perform better than traditional imputations in machine learning under different missing modalities settings. Finally, we analyse (for the first time in multimodal RSs) how feature homophily calculated on the item-item graph can influence our graph-based imputations.

Graph Neural Networks (GNNs) have proven to be highly effective in various graph learning tasks. A key characteristic of GNNs is their use of a fixed number of message-passing steps for all nodes in the graph, regardless of each node's diverse computational needs and characteristics. Through empirical real-world data analysis, we demonstrate that the optimal number of message-passing layers varies for nodes with different characteristics. This finding is further supported by experiments conducted on synthetic datasets. To address this, we propose Adaptive Depth Message Passing GNN (ADMP-GNN), a novel framework that dynamically adjusts the number of message passing layers for each node, resulting in improved performance. This approach applies to any model that follows the message passing scheme. We evaluate ADMP-GNN on the node classification task and observe performance improvements over baseline GNN models. Our code is publicly available at: https://github.com/abbahaddou/ADMP-GNN

Graph Neural Networks (GNNs) have emerged as the leading paradigm for learning over graph-structured data. However, their performance is limited by issues inherent to graph topology, most notably oversquashing and oversmoothing. Recent advances in graph rewiring aim to mitigate these limitations by modifying the graph topology to promote more effective information propagation. In this work, we introduce TRIGON, a novel framework that constructs enriched, non-planar triangulations by learning to select relevant triangles from multiple graph views. By jointly optimizing triangle selection and downstream classification performance, our method produces a rewired graph with markedly improved structural properties such as reduced diameter, increased spectral gap, and lower effective resistance compared to existing rewiring methods. Empirical results demonstrate that TRIGON outperforms state-of-the-art approaches on node classification tasks across a range of homophilic and heterophilic benchmarks.

This paper investigates the factuality of large language models (LLMs) as knowledge bases in the legal domain, in a realistic usage scenario: we allow for acceptable variations in the answer, and let the model abstain from answering when uncertain. First, we design a dataset of diverse factual questions about case law and legislation. We then use the dataset to evaluate several LLMs under different evaluation methods, including exact, alias, and fuzzy matching. Our results show that the performance improves significantly under the alias and fuzzy matching methods. Further, we explore the impact of abstaining and in-context examples, finding that both strategies enhance precision. Finally, we demonstrate that additional pre-training on legal documents, as seen with SaulLM, further improves factual precision from 63% to 81%.

Generally, items with missing modalities are dropped in multimodal recommendation. However, with this work, we question this procedure, highlighting that it would further damage the pipeline of any multimodal recommender system. First, we show that the lack of (some) modalities is, in fact, a widely-diffused phenomenon in multimodal recommendation. Second, we propose a pipeline that imputes missing multimodal features in recommendation by leveraging traditional imputation strategies in machine learning. Then, given the graph structure of the recommendation data, we also propose three more effective imputation solutions that leverage the item-item co-purchase graph and the multimodal similarities of co-interacted items. Our method can be plugged into any multimodal RSs in the literature working as an untrained pre-processing phase, showing (through extensive experiments) that any data pre-filtering is not only unnecessary but also harmful to the performance.

Finding the seed set that maximizes the influence spread over a network is a well-known NP-hard problem. Though a greedy algorithm can provide near-optimal solutions, the subproblem of influence estimation renders the solutions inefficient. In this work, we propose GLIE, a graph neural network that learns how to estimate the influence spread of the independent cascade. GLIE relies on a theoretical upper bound that is tightened through supervised training. Experiments indicate that it provides accurate influence estimation for real graphs up to 10 times larger than the train set. Subsequently, we incorporate it into two influence maximization techniques. We first utilize Cost Effective Lazy Forward optimization substituting Monte Carlo simulations with GLIE, surpassing the benchmarks albeit with a computational overhead. To improve computational efficiency we develop a provably submodular influence spread based on GLIE's representations, to rank nodes while building the seed set adaptively. The proposed algorithms are inductive, meaning they are trained on graphs with less than 300 nodes and up to 5 seeds, and tested on graphs with millions of nodes and up to 200 seeds. The final method exhibits the most promising combination of time efficiency and influence quality, outperforming several baselines.

Graph Neural Networks (GNNs) have succeeded in various computer science applications, yet deep GNNs underperform their shallow counterparts despite deep learning's success in other domains. Over-smoothing and over-squashing are key challenges when stacking graph convolutional layers, hindering deep representation learning and information propagation from distant nodes. Our work reveals that over-smoothing and over-squashing are intrinsically related to the spectral gap of the graph Laplacian, resulting in an inevitable trade-off between these two issues, as they cannot be alleviated simultaneously. To achieve a suitable compromise, we propose adding and removing edges as a viable approach. We introduce the Stochastic Jost and Liu Curvature Rewiring (SJLR) algorithm, which is computationally efficient and preserves fundamental properties compared to previous curvature-based methods. Unlike existing approaches, SJLR performs edge addition and removal during GNN training while maintaining the graph unchanged during testing. Comprehensive comparisons demonstrate SJLR's competitive performance in addressing over-smoothing and over-squashing.

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this problem are \textit{matrix factorization} and \textit{random walk}-based models. In this paper, we aim to bring together the best of both worlds, towards learning node representations. In particular, we propose a weighted matrix factorization model that encodes random walk-based information about nodes of the network. The benefit of this novel formulation is that it enables us to utilize kernel functions without realizing the exact proximity matrix so that it enhances the expressiveness of existing matrix decomposition methods with kernels and alleviate their computational complexities. We extend the approach with a multiple kernel learning formulation that provides the flexibility of learning the kernel as the linear combination of a dictionary of kernels in data-driven fashion. We perform an empirical evaluation on real-world networks, showing that the proposed model outperforms baseline node embedding algorithms in downstream machine learning tasks.

Graph Representation Learning (GRL) has become a key paradigm in network analysis, with a plethora of interdis-ciplinary applications. As the scale of networks increases, most of the widely used learning-based graph representation models also face computational challenges. While there is a recent effort toward designing algorithms that solely deal with scalability issues, most of them behave poorly in terms of accuracy on downstream tasks. In this paper, we aim to study models that balance the trade-off between efficiency and accuracy. In particular, we propose Nodesig, a scalable model that computes binary node representations. Nodesig exploits random walk diffusion probabilities via stable random projections towards efficiently computing embeddings in the Hamming space. Our extensive experimental evaluation on various networks has demonstrated that the proposed model achieves a good balance between accuracy and efficiency compared to well-known baseline models on the node classification and link prediction tasks.

Graph Neural Networks achieve state-of-the-art performance on a plethora of graph classification tasks, especially due to pooling operators, which aggregate learned node embeddings hierarchically into a final graph representation. However, they are not only questioned by recent work showing on par performance with random pooling, but also ignore completely higher-order connectivity patterns. To tackle this issue, we propose HoscPool, a clustering-based graph pooling operator that captures higher-order information hierarchically, leading to richer graph representations. In fact, we learn a probabilistic cluster assignment matrix end-to-end by minimising relaxed formulations of motif spectral clustering in our objective function, and we then extend it to a pooling operator. We evaluate HoscPool on graph classification tasks and its clustering component on graphs with ground-truth community structure, achieving best performance. Lastly, we provide a deep empirical analysis of pooling operators' inner functioning.

We address the problem of influence maximization when the social network is accompanied by diffusion cascades. In the literature, such information is used to compute influence probabilities, which is utilized by stochastic diffusion models in influence maximization. Motivated by the recent criticism on diffusion models and the galloping advancements in influence learning, we proposeIMINFECTOR(Influence Maximization with INFluencer vECTORs), a method that uses representations learned from diffusion cascades to perform model-independent influence maximization. The first part of our methodology is a multi-task neural network that learns embeddings of nodes that initiate cascades (influencer vectors) and embeddings of nodes that participate in them (susceptible vectors). The norm of an influencer vector captures a node’s aptitude to initiate lengthy cascades and is used to reduce the number of candidate seeds. The combination of influencer and susceptible vectors form the diffusion probabilities between nodes. These are used to reformulate the computation of the influence spread and propose a greedy solution to influence maximization that retains the theoretical guarantees. We apply our method in three sizable datasets and evaluate it using cascades from future time steps.IMINFECTOR’s scalability and accuracy outperform various competitive algorithms and metrics from the diverse landscape of influence maximization.

Social networks have become the main platforms for information dissemination. Nevertheless, due to the increasing number of users, social media platforms tend to be highly vulnerable to the propagation of disinformation - making the detection of fake news a challenging task. In this work, we focus on content-based methods for detecting fake news - casting the problem to a binary text classification one (an article corresponds to either fake news or not). In particular, our work proposes a graph-based semi-supervised fake news detection method based on graph neural networks. The experimental results indicate that the proposed methodology achieves better performance compared to traditional classification techniques, especially when trained on limited number of labeled articles1.

Some of the most effective influential spreader detection algorithms are unstable to small perturbations of the network structure. Inspired by bagging in Machine Learning, we propose the first Perturb and Combine (P&C) procedure for networks. It (1) creates many perturbed versions of a given graph, (2) applies a node scoring function separately to each graph, and (3) combines the results. Experiments conducted on real-world networks of various sizes with the k-core, generalized k-core, and PageRank algorithms reveal that P&C brings substantial improvements. Moreover, this performance boost can be obtained at almost no extra cost through parallelization. Finally, a bias-variance analysis suggests that P&C works mainly by reducing bias, and that therefore, it should be capable of improving the performance of all vertex scoring functions, including stable ones. An extended version of this paper is provided by [1].

Network embedding algorithms are able to learn latent feature representations of nodes, transforming networks into lower dimensional vector representations. Typical key applications, which have effectively been addressed using network embeddings, include link prediction, multilabel classification and community detection. In this paper, we propose Biased-Walk, a scalable, unsupervised feature learning algorithm that is based on biased random walks to sample context information about each node in the network. Our random-walk based sampling can behave as Breath-First-Search (BFS) and Depth-First-Search (DFS) samplings with the goal to capture homophily and role equivalence between the nodes in the network. We have performed a detailed experimental evaluation comparing the performance of the proposed algorithm against various baseline methods, on several datasets and learning tasks. The experiment results show that the proposed method outperforms the baseline ones in most of the tasks and datasets.

Graphs have been widely used as modeling tools in Natural Language Processing (NLP), Text Mining (TM) and Information Retrieval (IR). Traditionally, the unigram bag-of-words representation is applied; that way, a document is represented as a multiset of its terms, disregarding dependencies between the terms. Although several variants and extensions of this modeling approach have been proposed, the main weakness comes from the underlying term independence assumption; the order of the terms within a document is completely disregarded and any relationship between terms is not taken into account in the final task. To deal with this problem, the research community has explored various representations, and to this direction, graphs constitute a well-developed model for text representation. The goal of this tutorial is to offer a comprehensive presentation of recent methods that rely on graph-based text representations to deal with various tasks in Text Mining, NLP and IR.

Community detection constitutes an important task for investigating the internal structure of networks, with a plethora of applications in a wide range of disciplines. A particularly important point, which is rarely taken into account while developing community detection algorithms, is their sensitivity (or stability) to network uncertainty. In many cases, the input graph data is incomplete or noisy (e.g., due to noise introduced during the collection of the data or for privacy preserving reasons). Then, the following question arises: how stable are the results produced by an algorithm with respect to the uncertainty (i.e., noise level) of the input data? In this paper, we propose a quantitative way to address this problem. We have considered several graph perturbation models to introduce uncertainty to the graph. Then, we examine the sensitivity of an algorithm, with respect to functional and structural characteristics of the detected communities under various perturbation levels. We have studied the performance of some of the most widely used community detection algorithms in practice, and our experimental results indicate that random walk based community detection algorithms tend to be robust under various conditions of network uncertainty.

Graph mining is an important research area with a plethora of practical applications. Core decomposition in networks, is a fundamental operation strongly related to more complex mining tasks such as community detection, dense subgraph discovery, identification of influential nodes, network visualization, text mining, just to name a few. In this tutorial, we present in detail the concept and properties of core decomposition in graphs, the associated algorithms for its efficient computation and some of its most important applications.

Text categorization is an important task with plenty of applications, ranging from sentiment analysis to automated news classification. In this paper, we introduce a novel graph-based approach for text categorization. Contrary to the traditional Bag-of-Words model for document representation, we consider a model in which each document is represented by a graph that encodes relationships between the different terms. The importance of a term to a document is indicated using graph-theoretic node centrality criteria. The proposed weighting scheme is able to meaningfully capture the relationships between the terms that co-occur in a document, creating feature vectors that can improve the categorization task. We perform experiments in well-known document collections, applying popular classification algorithms. Our preliminary results indicate that the proposed graph-based weighting mechanism is able to outperform existing frequency-based term weighting criteria, under appropriate parameter setting.

Given a large social graph, how can we model the engagement properties of nodes? Can we quantify engagement both at node level as well as at graph level? Typically, engagement refers to the degree that an individual participates (or is encouraged to participate) in a community and is closely related to the important property of nodes' departure dynamics, i.e., the tendency of individuals to leave the community. In this paper, we build upon recent work in the field of game theory, where the behavior of individuals (nodes) is modeled by a technology adoption game. That is, the decision of a node to remain engaged in the graph is affected by the decision of its neighbors, and the "best practice" for each individual is captured by its core number - as arises from the k-core decomposition. After modeling and defining the engagement dynamics at node and graph level, we examine whether they depend on structural and topological features of the graph. We perform experiments on a multitude of real graphs, observing interesting connections with other graph characteristics, as well as a clear deviation from the corresponding behavior of random graphs. Furthermore, similar to the well known results about the robustness of real graphs under random and targeted node removals, we discuss the implications of our findings on a special case of robustness - regarding random and targeted node departures based on their engagement level.

Graphs constitute a dominant data structure and appear essentially in all forms of information. Examples are the Web graph, numerous social networks, protein interaction networks, terms dependency graphs and network topologies. The main features of these graphs are their huge volume and rate of change. Presumably, there is important hidden knowledge in the macroscopic topology and features of these graphs. A cornerstone issue here is the detection and evaluation of communities -- bearing multiple and diverse semantics. The tutorial reports the basic models of graph structures for undirected, directed and signed graphs and their properties. Next we offer a thorough review of fundamental methods for graph clustering and community detection, on both undirected and directed graphs. Then we survey community evaluation measures, including both the individual node based ones as well as those that take into account aggregate properties of communities. A special mention is made on approaches that capitalize on the concept of degeneracy (k-cores and extensions), as a novel means of community detection and evaluation. We justify the above foundational framework with applications on citation graphs, trust networks and protein graphs.

Given a large social graph, like a scientific collaboration network, what can we say about its robustness? Can we estimate a robustness index for a graph quickly? If the graph evolves over time, how these properties change? In this work, we are trying to answer the above questions studying the expansion properties of large social graphs. First, we present a measure which characterizes the robustness properties of a graph, and serves as global measure of the community structure (or lack thereof). We study how these properties change over time and we show how to spot outliers and anomalies over time. We apply our method on several diverse real networks with millions of nodes. We also show how to compute our measure efficiently by exploiting the special spectral properties of real-world networks.