Related papers: Node-neighbor subnetworks and Hk-core decompositio…
Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays…
Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions…
The life of the modern world essentially depends on the work of the large artificial homogeneous networks, such as wired and wireless communication systems, networks of roads and pipelines. The support of their effective continuous…
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts for the maximal smallest degree of a subgraph containing a…
This paper presents HGEN that pioneers ensemble learning for heterogeneous graphs. We argue that the heterogeneity in node types, nodal features, and local neighborhood topology poses significant challenges for ensemble learning,…
The process of destroying a complex network through node removal has been the subject of extensive interest and research. Node loss typically leaves the network disintegrated into many small and isolated clusters. Here we show that these…
Network alignment is useful for multiple applications that require increasingly large graphs to be processed. Existing research approaches this as an optimization problem or computes the similarity based on node representations. However,…
Multilayer networks are in the focus of the current complex network study. In such networks multiple types of links may exist as well as many attributes for nodes. To fully use multilayer -- and other types of complex networks in…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous…
In this paper, we investigate the parallelization of $k$-core decomposition, a method used in graph analysis to identify cohesive substructures and assess node centrality. Although efficient sequential algorithms exist for this task, the…
We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning…
Modern neural network technologies, including large language models, have achieved remarkable success in various applied artificial intelligence applications, however, they face a range of fundamental limitations. Among them are…
Let $G=(V, E)$ be a connected graph, a subset $S\subseteq V(G)$ is called an $R^{g}$-vertex-cut of $G$ if $G-F$ is disconnected and any vertex in $G-F$ has at least $g$ neighbours in $G-F$. The $R^{g}$-vertex-connectivity is the size of the…
The neighbor connectivity of a graph $G$ is the least number of vertices such that removing their closed neighborhoods from $G$ results in a graph that is disconnected, complete or empty. If a~graph is used to model the topology of an…
Hessian captures important properties of the deep neural network loss landscape. Previous works have observed low rank structure in the Hessians of neural networks. In this paper, we propose a decoupling conjecture that decomposes the…
Graph Neural Networks (GNNs) have been predominant for graph learning tasks; however, recent studies showed that a well-known graph algorithm, Label Propagation (LP), combined with a shallow neural network can achieve comparable performance…
Motivated by the relevance of higher-order interactions in quantum physics and materials science at the nanoscale, recently a model has been introduced for new classes of networks that grow by the geometrically constrained aggregation of…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…