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The myriad complex systems with multiway interactions motivate the extension of graph-based pairwise connections to higher-order relations. In particular, the simplicial complex has inspired generalizations of graph neural networks (GNNs)…
We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…
Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem…
Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with non-negative Lin-Lu-Yau curvature is equal to its minimum…
Given a finite, simple graph $G$, the $k$-component order edge connectivity of $G$ is the minimum number of edges whose removal results in a subgraph for which every component has order at most $k-1$. In general, determining the…
Cross-graph node classification, utilizing the abundant labeled nodes from one graph to help classify unlabeled nodes in another graph, can be viewed as a domain generalization problem of graph neural networks (GNNs) due to the structure…
We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time…
For a connected graph, a {\em minimum vertex separator} is a minimum set of vertices whose removal creates at least two connected components. The vertex connectivity of the graph refers to the size of the minimum vertex separator and a…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…
We study a problem of reconstruction of connected graphs where the input gives all subsets of size k that induce a connected subgraph. Originally introduced by Bastide et al. (WG 2023) for triples ($k=3$), this problem received…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
Graph augmentation methods play a crucial role in improving the performance and enhancing generalisation capabilities in Graph Neural Networks (GNNs). Existing graph augmentation methods mainly perturb the graph structures, and are usually…
To investigate hyperbinary expansions of a nonnegative integer~$n$, an edge-labeled directed graph $A(n)$ has recently been introduced. After pointing out some new simple facts about its cyclomatic number, we give a relatively simple…
We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation…
We consider edge insertion and deletion operations that increase the connectivity of a given planar straight-line graph (PSLG), while minimizing the total edge length of the output. We show that every connected PSLG $G=(V,E)$ in general…