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Zero forcing is an iterative coloring process on a graph that has been widely used in such different areas as the modelling of propagation phenomena in networks and the study of minimum rank problems in matrices and graphs. This paper deals…

Combinatorics · Mathematics 2021-09-24 Josep Fàbrega , Jaume Martí-Farré , Xavier Muñoz

A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this paper…

Combinatorics · Mathematics 2016-05-20 Maciej Kalkowski , Michał Karoński , Florian Pfender

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

Discrete Mathematics · Computer Science 2020-12-08 Marzieh Eidi , Amirhossein Farzam , Wilmer Leal , Areejit Samal , Jürgen Jost

We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is…

Social and Information Networks · Computer Science 2022-06-03 Marios Papachristou , Jon Kleinberg

Let $H=(V,E)$ be a hypergraph, where $V$ is a set of vertices and $E$ is a set of non-empty subsets of $V$ called edges. If all edges of $H$ have the same cardinality $r$, then $H$ is a $r$-uniform hypergraph; if $E$ consists of all…

Combinatorics · Mathematics 2018-07-18 Yingzhi Tian , Liqiong Xu , Hong-Jian Lai , Jixiang Meng

Simplicial surfaces describe the incidence relations between vertices, edges and faces of triangulated 2-dimensional manifolds in a purely combinatorial way. By considering only the incidences of edges and faces, simplicial surfaces are…

Combinatorics · Mathematics 2025-06-26 Meike Weiß , Alice C. Niemeyer

An EPG-representation of a graph $G$ is a collection of paths in a plane square grid, each corresponding to a single vertex of $G$, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In…

Discrete Mathematics · Computer Science 2017-11-15 Martin Pergel , Paweł Rzążewski

This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency…

Combinatorics · Mathematics 2012-12-27 Tyler Friesen , Vassily Manturov

F-index of a graph is the sum of the cube of the degrees of the vertices. In this paper, we investigate the F-indices of unicyclic graphs by introducing some transformation, and characterize the unicyclic graphs with the first five largest…

Combinatorics · Mathematics 2016-09-06 Ruhul Amin , Sk. Md. Abu Nayeem

A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-transitive graph is maximally edge-connected. We generalise…

Combinatorics · Mathematics 2023-10-02 Andrea C. Burgess , Robert D. Luther , David A. Pike

Among all uniform hypergraphs with even uniformity, the odd-transversal or odd-bipartite hypergraphs are more close to bipartite simple graphs from the viewpoint of both structure and spectrum. A hypergraph is called minimal…

Combinatorics · Mathematics 2021-08-31 Yi-Zheng Fan , Yi Wang , Jiang-Chao Wan

Co-occurence networks can be adequately modeled by hyper-bag-graphs (hb-graphs for short). A hb-graph is a family of multisets having same universe, called the vertex set. An efficient exchange-based diffusion scheme has been previously…

Social and Information Networks · Computer Science 2020-03-17 Xavier Ouvrard , Jean-Marie Le Goff , Stéphane Marchand-Maillet

We consider undirected simple finite graphs. The sets of vertices and edges of a graph $G$ are denoted by $V(G)$ and $E(G)$, respectively. For a graph $G$, we denote by $\delta(G)$ and $\eta(G)$ the least degree of a vertex of $G$ and the…

Combinatorics · Mathematics 2013-07-05 N. N. Davtyan , R. R. Kamalian

The two graphs of the title both have vertex set G. In the intersection power graph, x and y are joined if some non-identity element is a power of both; in the power graph, x and y joined if one is a power of the other. Thus the power graph…

Combinatorics · Mathematics 2025-09-05 Sudip Bera , Peter J. Cameron

Let V denote a set of N vertices. To construct a "hypergraph process", create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with arbitrary probability generating function r(x),…

Probability · Mathematics 2007-05-23 R. W. R. Darling , D. A. Levin , J. R. Norris

Hypergraphs have been a powerful tool to represent higher-order interactions, where hyperedges can connect an arbitrary number of nodes. Quantifying the relative importance of nodes and hyperedges in hypergraphs is a fundamental problem in…

Social and Information Networks · Computer Science 2026-03-03 Qing Xu , Chunmeng Liu , Changjiang Bu , Jihong Shen

Hypergraphs extend traditional networks by capturing multi-way or group interactions. Given the complexity of hypergraph data and the wide range of methodology available for pairwise network analysis, hypergraph data is often projected onto…

Social and Information Networks · Computer Science 2025-06-23 Timothy LaRock , Renaud Lambiotte

Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…

Combinatorics · Mathematics 2016-11-25 David Ellison , Ruxandra Marinescu-Ghemeci , Cerasela Tanasescu

The graph invariant examined in this paper is the largest eigenvalue of the adjacency matrix of a graph. Previous work demonstrates the tight relationship between this invariant, the birth and death rate of a contagion spreading on the…

Social and Information Networks · Computer Science 2022-10-27 V. Cherniavskyi , G. Dennis , S. R. Kingan

In this paper, our goal is to characterize two graph classes based on the properties of minimal vertex (edge) separators. We first present a structural characterization of graphs in which every minimal vertex separator is a stable set. We…

Discrete Mathematics · Computer Science 2011-03-16 Mrinal Kumar , Gaurav Maheswari , N. Sadagopan