Related papers: Node-neighbor subnetworks and Hk-core decompositio…
We introduce a $k$-leaf removal algorithm as a generalization of the so-called leaf removal algorithm. In this pruning algorithm, vertices of degree smaller than $k$, together with their first nearest neighbors and all incident edges are…
The $H$-Free Edge Deletion problem asks, for a given graph $G$ and an integer $k$, whether it is possible to delete at most $k$ edges from $G$ to make it $H$-free, that is, not containing $H$ as an induced subgraph. The $H$-Free Edge…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
Recent advances in the field of network representation learning are mostly attributed to the application of the skip-gram model in the context of graphs. State-of-the-art analogues of skip-gram model in graphs define a notion of…
Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were…
Despite the success of Heterogeneous Graph Neural Networks (HGNNs) in modeling real-world Heterogeneous Information Networks (HINs), challenges such as expressiveness limitations and over-smoothing have prompted researchers to explore Graph…
The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…
The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks…
Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…
Planar homography, with eight degrees of freedom (DOFs), is fundamental in numerous computer vision tasks. While the positional offsets of four corners are widely adopted (especially in neural network predictions), this parameterization…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph…
Decycling and dismantling of complex networks are underlying many important applications in network science. Recently these two closely related problems were tackled by several heuristic algorithms, simple and considerably sub-optimal, on…
A popular model to measure network stability is the $k$-core, that is the maximal induced subgraph in which every vertex has degree at least $k$. For example, $k$-cores are commonly used to model the unraveling phenomena in social networks.…
Neural network decoding algorithms are recently introduced by Nachmani et al. to decode high-density parity-check (HDPC) codes. In contrast with iterative decoding algorithms such as sum-product or min-sum algorithms in which the weight of…
Multi-layer networks or multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multi-layer networks are especially useful when describing the systems with several kinds…
The $k$-core decomposition in a graph is a fundamental problem for social network analysis. The problem of $k$-core decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on $k$-core…
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…
The modular decomposition of a graph $G$ is a natural construction to capture key features of $G$ in terms of a labeled tree $(T,t)$ whose vertices are labeled as "series" ($1$), "parallel" ($0$) or "prime". However, full information of $G$…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Network structure or topology is the basis for understanding complex systems. Recently, higher-order structures have been considered as a new research direction that can provide new perspectives and phenomena. However, most existing studies…