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A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
It is fundamental for science and technology to be able to predict chemical reactions and their properties. To achieve such skills, it is important to develop good representations of chemical reactions, or good deep learning architectures…
The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks,…
Scene graph generation aims to produce structured representations for images, which requires to understand the relations between objects. Due to the continuous nature of deep neural networks, the prediction of scene graphs is divided into…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
Higher-order interactions (HOIs) in complex systems, such as scientific collaborations, multi-protein complexes, and multi-user communications, are commonly modeled as hypergraphs, where each hyperedge (i.e., a subset of nodes) represents…
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to…
Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two…
Hypergraphs tackle the limitations of traditional graphs by introducing {\em hyperedges}. While graph edges connect only two nodes, hyperedges connect an arbitrary number of nodes along their edges. Also, the underlying message-passing…
Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We…
Node classification is one of the hottest tasks in graph analysis. Though existing studies have explored various node representations in directed and undirected graphs, they have overlooked the distinctions of their capabilities to capture…
A graph is a powerful concept for representation of relations between pairs of entities. Data with underlying graph structure can be found across many disciplines and there is a natural desire for understanding such data better. Deep…
We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One…
Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…
We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree…