Related papers: Graph Theory and Optimization Problems for Very La…
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…
Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding…
Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…
In this paper, we describe {\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative…
This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of…
Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
Graph neural networks have emerged as a leading architecture for many graph-level tasks, such as graph classification and graph generation. As an essential component of the architecture, graph pooling is indispensable for obtaining a…
Network structure optimization is a fundamental task in complex network analysis. However, almost all the research on Bayesian optimization is aimed at optimizing the objective functions with vectorial inputs. In this work, we first present…
Graphs are an essential data structure utilized to represent relationships in real-world scenarios. Prior research has established that Graph Neural Networks (GNNs) deliver impressive outcomes in graph-centric tasks, such as link prediction…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite…
Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been…
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…
Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of…