Related papers: Node-neighbor subnetworks and Hk-core decompositio…
This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a…
Core decomposition is an efficient building block for various graph analysis tasks such as dense subgraph discovery and identifying influential nodes. One crucial weakness of the core decomposition is its sensitivity to changes in the…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
The notion of $\mathcal{H}$-treewidth, where $\mathcal{H}$ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of $\mathcal{H}$-treewidth at most $k$…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
We present a new method for assessing and measuring homophily in networks whose nodes have categorical attributes, namely when the nodes of networks come partitioned into classes (colors). We probe this method in two different classes of…
Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…
K-cores are maximal induced subgraphs where all vertices have degree at least k. These dense patterns have applications in community detection, network visualization and protein function prediction. However, k-cores can be quite unstable to…
Many real-world data can be represented as heterogeneous graphs with different types of nodes and connections. Heterogeneous graph neural network model aims to embed nodes or subgraphs into low-dimensional vector space for various…
The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells…
We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…
Previous research has proven that the set of maps implemented by neural networks with a ReLU activation function is identical to the set of piecewise linear continuous maps. Furthermore, such networks induce a hyperplane arrangement…
From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a…
Graph neural networks (GNNs) have been proved powerful in graph-oriented tasks. However, many real-world graphs are heterophilous, challenging the homophily assumption of classical GNNs. To solve the universality problem, many studies…
The decoupled Graph Convolutional Network (GCN), a recent development of GCN that decouples the neighborhood aggregation and feature transformation in each convolutional layer, has shown promising performance for graph representation…
Simplicial homology is a tool that provides a mathematical way to compute the connectivity and the coverage of a cellular network without any node location information. In this article, we use simplicial homology in order to not only…
Given an undirected graph, the $k$-core is a subgraph in which each node has at least $k$ connections. This is widely used in graph analytics to identify core subgraphs within a larger graph. The sequential $k$-core decomposition algorithm…
Graph representation learning aim at integrating node contents with graph structure to learn nodes/graph representations. Nevertheless, it is found that many existing graph learning methods do not work well on data with high heterophily…
We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By…
This paper proposes efficient solutions for $k$-core decomposition with high parallelism. The problem of $k$-core decomposition is fundamental in graph analysis and has applications across various domains. However, existing algorithms face…