Related papers: Deterministic Graph-Walking Program Mining
We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields.
Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
Predicting interactions between structured entities lies at the core of numerous tasks such as drug regimen and new material design. In recent years, graph neural networks have become attractive. They represent structured entities as graphs…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…
We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…
Message-passing graph neural networks (GNNs) excel at capturing local relationships but struggle with long-range dependencies in graphs. In contrast, graph transformers (GTs) enable global information exchange but often oversimplify the…
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…
We present the implementation of an algorithm for graph isomorphism testing, based on ideas about number of walks (of sufficiently large length) between vertices. The algorithm is expanded for strongly regular graphs (SRG-s) by testing the…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
The verification community has studied dynamic data structures primarily in a bottom-up way by analyzing pointers and the shapes induced by them. Recent work in fields such as separation logic has made significant progress in extracting…
Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random…
Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…