Related papers: Graph Lineages and Skeletal Graph Products
Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
Context: Edge graphs are graphs whose edges are labelled with identifiers, and nodes can have multiple edges between them. They are used to model a wide range of systems, including networks with distances or degrees of connection and…
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural…
The ability to generate novel, diverse, and realistic 3D shapes along with associated part semantics and structure is central to many applications requiring high-quality 3D assets or large volumes of realistic training data. A key challenge…
Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Graph generation techniques are increasingly being adopted for drug discovery. Previous graph generation approaches have utilized relatively small molecular building blocks such as atoms or simple cycles, limiting their effectiveness to…
Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
Large graphs are present in a variety of domains, including social networks, civil infrastructure, and the physical sciences to name a few. Graph generation is similarly widespread, with applications in drug discovery, network analysis and…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale…
The degree sequence of a graph is a numerical method to characterize the properties of graphs. Generalized forms of degree sequences exist for complete graphs and complete graphs. Nikolopolus et al. characterized the number of spanning…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…
Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…
In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons…