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Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph…
An oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure. In this paper we obtain a combinatorial characterization of…
Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex…
Dynamic graph anomaly detection (DGAD) is essential for identifying anomalies in evolving graphs across domains such as finance, traffic, and social networks. Recently, generalist graph anomaly detection (GAD) models have shown promising…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
Contrastive learning leverages data augmentation to develop feature representation without relying on large labeled datasets. However, despite its empirical success, the theoretical foundations of contrastive learning remain incomplete,…
Community detection has long been an important yet challenging task to analyze complex networks with a focus on detecting topological structures of graph data. Essentially, real-world graph data contains various features, node and edge…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
Semi-supervised graph anomaly detection (GAD) has recently received increasing attention, which aims to distinguish anomalous patterns from graphs under the guidance of a moderate amount of labeled data and a large volume of unlabeled data.…
A broad range of applications involve signals with irregular structures that can be represented as a graph. As the underlying structures can change over time, the tracking dynamic graph topologies from observed signals is a fundamental…
Graph anomaly detection has attracted considerable attention from various domain ranging from network security to finance in recent years. Due to the fact that labeling is very costly, existing methods are predominately developed in an…
Online monitoring user cardinalities (or degrees) in graph streams is fundamental for many applications. For example in a bipartite graph representing user-website visiting activities, user cardinalities (the number of distinct visited…
To address the peculiarities of directed and/or signed graphs, new Laplacian operators have emerged. For instance, in the case of directionality, we encounter the magnetic operator, dilation (which is underexplored), operators based on…
Dynamic graph anomaly detection (DGAD) is critical for many real-world applications but remains challenging due to the scarcity of labeled anomalies. Existing methods are either unsupervised or semi-supervised: unsupervised methods avoid…
The hyperbolic space, characterized by a constant negative curvature and exponentially expanding space, aligns well with the structural properties of heterogeneous graphs. However, although heterogeneous graphs inherently possess diverse…
Convolutional neural networks are nowadays witnessing a major success in different pattern recognition problems. These learning models were basically designed to handle vectorial data such as images but their extension to non-vectorial and…
Recent years have witnessed tremendous interest in deep learning on graph-structured data. Due to the high cost of collecting labeled graph-structured data, domain adaptation is important to supervised graph learning tasks with limited…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…