Related papers: The method of hypergraph containers
While there has been tremendous activity in the area of statistical network inference on graphs, hypergraphs have not enjoyed the same attention, on account of their relative complexity and the lack of tractable statistical models. We…
We introduce a class of budgeted prize-collecting covering subgraph problems. For an input graph with prizes on the vertices and costs on the edges, the aim of these problems is to find a connected subgraph such that the cost of its edges…
Given an arbitrary hypergraph $\mathcal{H}$, we may glue to $\mathcal{H}$ a family of hypergraphs to get a new hypergraph $\mathcal{H}'$ having $\mathcal{H}$ as an induced subhypergraph. In this paper, we introduce three gluing techniques…
We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual…
Let $G$ be a connected undirected graph on $n$ vertices with no loops but possibly multiedges. Given an arithmetical structure $(\textbf{r}, \textbf{d})$ on $G$, we describe a construction which associates to it a graph $G'$ on $n-1$…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on…
We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It…
We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We…
Community detection refers to the problem of clustering the nodes of a network (either graph or hypergrah) into groups. Various algorithms are available for community detection and all these methods apply to uncensored networks. In…
Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
A growing set of on-line applications are generating data that can be viewed as very large collections of small, dense social graphs -- these range from sets of social groups, events, or collaboration projects to the vast collection of…
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…
Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…
We generalize ultraproducts and local-global limits of graphs to hypergraphs and other structures. We show that the local statistics of an ultraproduct of a sequence of hypergraphs are the ultralimits of the local statistics of the…
We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Half graphs and their variants, such as ladders, semi-ladders and co-matchings, are combinatorial objects that encode total orders in graphs. Works by Adler and Adler (Eur. J. Comb.; 2014) and Fabia\'nski et al. (STACS; 2019) prove that in…