Related papers: Exploring complex networks via topological embeddi…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse…

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…

Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…

Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been…

TopoDetect is a Python package that allows the user to investigate if important topological features, such as the Degree of the nodes, their Triangle Count, or their Local Clustering Score, are preserved in the embeddings of graph…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Graphs can model real-world, complex systems by representing entities and their interactions in terms of nodes and edges. To better exploit the graph structure, graph neural networks have been developed, which learn entity and edge…

Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…

Graph Neural Networks (GNNs) have excelled in predicting graph properties in various applications ranging from identifying trends in social networks to drug discovery and malware detection. With the abundance of new architectures and…

Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at the assumptions they make on the underlying network. We investigate this question from the perspective of network…

Many online networks are measured and studied via sampling techniques, which typically collect a relatively small fraction of nodes and their associated edges. Past work in this area has primarily focused on obtaining a representative…

Graph, as an important data representation, is ubiquitous in many real world applications ranging from social network analysis to biology. How to correctly and effectively learn and extract information from graph is essential for a large…