Hyperbolic geometry has recently emerged as a powerful alternative to Euclidean spaces for representing graph-structured data, particularly due to its ability to capture hierarchical and scale-free structures with low distortion. This paper presents a comprehensive survey of hyperbolic graph embedding methods, providing both a conceptual overview and a systematic taxonomy of existing approaches. Beyond a purely descriptive survey, our work is specifically designed to address key limitations of existing surveys by incorporating a unified and reproducible experimental perspective. Unlike prior surveys, which mainly focus on theoretical foundations, our work places a particular emphasis on anomaly detection in graphs as a unifying and practically relevant evaluation task. To this end, we combine theoretical analysis with a unified evaluation protocol and a practical and reproducible evaluation framework, including a publicly available open-source library that provides a common platform implementing the most representative hyperbolic embedding methods. Using this framework, we conduct extensive experiments on diverse real-world datasets to systematically assess the effectiveness of hyperbolic representations for anomaly detection and to compare them against Euclidean baselines.

Graph-based anomaly detection has emerged as a powerful tool in cybersecurity for identifying malicious activities within computer systems and networks. While existing approaches often rely on embedding graphs in Euclidean space, recent studies have suggested that hyperbolic space provides a more suitable geometry for capturing the inherent hierarchical and complex relationships present in graph data. In this paper, we explore the efficacy of hyperbolic graph embedding for anomaly detection in the context of cybersecurity. We conduct a comparison of six state-of-the-art hyperbolic graph embedding methods, evaluating their performance on a well-known intrusion detection dataset. Our analysis reveals the strengths and limitations of each method, demonstrating the potential of hyperbolic graph embedding for enhancing security.

We consider the problem of data augmentation for graph neural networks. While other areas of deep learning, especially computer vision, has benefited greatly from data augmentation, graph deep learning is limited by the complex structure and nodes dependency of graph datasets. The works studying data augmentation for graphs focus on ways to train the model on generated graphs or disturb the original one by masking attributes or dropping nodes/edges. Our work studies data augmentation for graphs in the latent space. We propose an architecture to train a graph neural network including a data augmentation component which also has a denoising and structure enhancer function. Our architecture leverages the supervised feedback to introduce the graph neural network component to a new latent representation of the graph with lesser irrelevant connections on the graph domain. We perform experiments on datasets from several domains with different sizes and show that our architecture improves the performance over a variety of plain graph neural networks on node classification.

We introduce a new graph sparsification method that targets the neighborhood information available for each node. Our approach is motivated by the fact that neighborhood information is used by several mining and learning tasks on graphs as well as reachability queries. The result of our sparsification technique is a sparsified graph that can be used instead of the original graph in the above tasks while still ensuring fairly good approximations for the results. Moreover, our sparsification method allows users to control the size of the resulting sparsified graph by adjusting the amount of information loss tolerated by the targeted applications. Our extensive experiments conducted on various real and synthetic graphs show that our sparsification considerably reduces the size of the graphs by achieving 40% sparsification rate on average on several input graphs. Furthermore, in the experimental study we show the utility and efficiency of our sparsification algorithm for notable data-driven tasks, such as node classification, graph classification and shortest path approximations.

We introduce the γ -clustering problems, which are variants of the well-known Cluster Editing/Deletion/Completion problems, and defined as: given a graph G , how many edges must be edited in G , deleted from G , or added to G in order to have a disjoint union of γ -quasi-cliques. We provide here the complete complexity classification of these problems along with FPT algorithms parameterized by the number of modifications, for the NP -complete problems. We also study here a variant of these problems where the number of final clusters is a fixed constant, obtaining mostly the same results regarding classical and parameterized complexity.

Learning low dimensional representations requires an expressive technique capable of capturing the different features for nodes, the relationship between nodes in the network and thus their similarities. However, many existing embedding techniques focus only on capturing the structural patterns in the network by randomly sampling the nodes in the neighborhood of the target node. To deal with this issue, we propose DSNCR, a node representation framework which uses the non-linear node attributes as well as their neighbourhood structural information to capture nodes similarities. This approach computes a semi-supervised regression analysis on the node attributes to guide a flexible probability walk procedure, such that different neighbourhoods are explored to capture rich network attributes and structures in a learned embedding. We verify the effectiveness of our model on link prediction and node classification tasks using real-life benchmark datasets, for which our technique performs better than existing embedding methods.

Abstract We present a silent self-stabilizing distributed algorithm computing a maximal $\ p$-star decomposition of the underlying communication network. Under the unfair distributed scheduler, the most general scheduler model, the algorithm converges in at most $12\Delta m + \mathcal{O}(m+n)$ moves, where $m$ is the number of edges, $n$ is the number of nodes and $\Delta $ is the maximum node degree. Regarding the time complexity, we obtain the following results: our algorithm outperforms the previously known best algorithm by a factor of $\Delta $ with respect to the move complexity. While the round complexity for the previous algorithm was unknown, we show a $5\big \lfloor \frac{n}{p+1} \big \rfloor +5$ bound for our algorithm.

In condition-based maintenance, real-time observations are crucial for on-line health assessment. When the monitoring system is a wireless sensor network (WSN), data loss becomes highly probable and this affects the quality of the remaining useful life prediction. In this paper, we present a fully distributed algorithm that ensures fault tolerance and recovers data loss in WSNs. We first theoretically analyze the algorithm and give correctness proofs, then provide simulation results and show that the algorithm is (i) able to ensure data recovery with a low failure rate and (ii) preserves the overall energy for dense networks.

We present GraphExploiter, a tool to import, visualize and manage data by representing them in a graph structure. The aim of this platform is (i) to facilitate the creation of graphs from real data sets, (ii) to propose an efficient tool of scalable visualization and (iii) to allow a user to import easily its own graph algorithms to the platform.

Lifetime optimization becomes a commonplace feature of wireless sensor networks. In addition, as the scale is expanding, node reliabilities gradually become dynamically heterogeneous over time even if sensor nodes are symmetric by design. At the same time, as sensor nodes get smaller and approach technological limits, they suffer from increased susceptibility to wear-out which becomes a real problem as complex sensor networks with many nodes operate in unsafe and harsh environments for long times. Con sequently, there is an increasing need for developing techniques to achieve more reliability, i.e., increase the net work's operational time. In this paper, we introduce an efficient distributed failure-aware strategy (on-line solution) using probabilistic Weibull distribution to resist to frequent and unexpected fail-silent/fail-stop node failures. We provide a comprehensive set of experimental results, that fully demonstrate the usefulness of the proposed solution.

The study of emerged community structures is an important challenge in networks analysis. In fact, several methods have been proposed in the literature to statistically determine the signification of discovered structures. Nevertheless, most of existing analysis models consider only the structural aspect of emerged communities. In our study, we give interest to robustness study of emerged communities in resource exchange networks. More precisely, we consider the emerged communities in the induced graph by all the exchanges in these networks. Hence, rather than examining the robustness only on the structural properties of the graph, we give focus to the parameters that allow the emergence of community structures. In fact, perturbing these parameters might destroy most of the obtained properties at the emerged level. To the best of our knowledge, robustness of networks has never been considered from this angle before. In this paper, we study the impact of perturbing the content, the interest and the profile of nodes on the emerged social communities in resource exchange networks. We show how these alterations affect both structure and information supported by the emerged structures.

In this paper, we deal with the problem of distributed data fusion in unsafe large-scale sensor networks. Data fusion application is the phase of processing the collected data by sensor nodes before sending it the end user. During this phase, resource failures are more likely to occur and can have an adverse effect on the application. Hence, we introduce first an efficient self-stabilizing algorithm to achieve/ensure the convergence of node states to the average of the initial measurements of the network. Next, we present a fault tolerant scheme to resist to frequent and unexpected not concomitant fail-silent/fail-stop node failures. The major contribution of this paper is the design of an analytical expression (an upper bound) of the actual number of moves/iterations required by the algorithm. We provide a comprehensive set of experimental results, that fully demonstrate the usefulness of the proposed schemes.

The social networks and the study of communities of interest became an actual challenge in several research areas. Community detection techniques have found a large number of practical applications as a method to simplify networks since the number of clusters is often much smaller than the number of nodes. In this paper, we study two aspects. In the first part, we focus on the induced social interactions by the communication between the individuals (peers) of a network in order to extract properties of the resultant community structures. Plenty of communication protocols were defined to allow and improve the data exchange between the different peers of the network [13][19][18]. The second part of our work concerns the study of the robustness of emerging communities.