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Graph neural networks (GNNs) are shown to be successful in modeling applications with graph structures. However, training an accurate GNN model requires a large collection of labeled data and expressive features, which might be inaccessible…
The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…
Inspired by the generation power of generative adversarial networks (GANs) in image domains, we introduce a novel hierarchical architecture for learning characteristic topological features from a single arbitrary input graph via GANs. The…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…
A graph is a very common and powerful data structure used for modeling communication and social networks. Models that generate graphs with arbitrary features are important basic technologies in repeated simulations of networks and…
This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are…
As the scale of networked control systems increases and interactions between different subsystems become more sophisticated, questions of the resilience of such networks increase in importance. The need to redefine classical system and…
Graph learning has become essential in various domains, including recommendation systems and social network analysis. Graph Neural Networks (GNNs) have emerged as promising techniques for encoding structural information and improving…
Deep neural networks for graphs have emerged as a powerful tool for learning on complex non-euclidean data, which is becoming increasingly common for a variety of different applications. Yet, although their potential has been widely…
Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our…
There is a profound connection between copositive matrices and graph theory. Copositive matrices provide a powerful tool for formulating and solving various challenging graph-related problems. Conversely, graph theory provides a rich set of…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…
A construction sequence for a graph is a listing of the elements of the graph (the set of vertices and edges) such that each edge follows both its endpoints. The construction number of the graph is the number of such sequences. We determine…
Connections between structural graph theory and finite model theory recently gained a lot of attention. In this setting, many interesting questions remain on the properties of dependent (NIP) hereditary classes of graphs, in particular…
Traditional model-based diagnosis relies on constructing explicit system models, a process that can be laborious and expertise-demanding. In this paper, we propose a novel framework that combines concepts of model-based diagnosis with deep…