Related papers: Constructions of betweenness-uniform graphs from t…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…
The \emph{thinness} of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many…
A middle-cube is an induced subgraph consisting of nodes at the middle two layers of a hypercube. The middle-cubes are related to the well-known Revolving Door (Middle Levels) conjecture. We study the middle-cube graph by completely…
The goal of this paper is to present a centrality measurement for the nodes of a hypergraph, by using existing literature which extends eigenvector centrality from a graph to a hypergraph, and literature which give a general centrality…
Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well…
We introduce the notion of \emph{bounded diameter arboricity}. Specifically, the \emph{diameter-$d$ arboricity} of a graph is the minimum number $k$ such that the edges of the graph can be partitioned into $k$ forests each of whose…
The problem of betweenness centrality remains a fundamental unsolved problem in complex networks. After a pioneering work by Barthelemy, it has been well-accepted that the maximal betweenness-degree ($b$-$k$) exponent for scale-free (SF)…
Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In the present paper, we show that functionality is bounded for box intersection graphs in…
A hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. This study derives hardness results for the classification variant of graph isomorphism in the message-passing model (MPNN). MPNN…
The study of structural graph width parameters like tree-width, clique-width and rank-width has been ongoing during the last five decades, and their algorithmic use has also been increasing [Cygan et al., 2015]. New width parameters…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
Tree-decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. The main property of tree-decompositions is the width (the maximum size of a bag minus 1). We show that every graph has a…
A load applied to a jammed frictional granular system will be localized into a network of force chains making inter-particle connections throughout the system. Because such systems are typically under-constrained, the observed force network…
A \textit{$t$-unit-bar representation} of a graph $G$ is an assignment of sets of at most $t$ horizontal unit-length segments in the plane to the vertices of $G$ so that (1) all of the segments are pairwise nonintersecting, and (2) two…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
Betweenness centrality, measured by the number of times a vertex occurs on all shortest paths of a graph, has been recognized as a key indicator for the importance of a vertex in the network. However, the betweenness of a vertex is often…
A new 2-parameter family of central structures in trees, called central forests, is introduced. Minieka's $m$-center problem and McMorris's and Reid's central-$k$-tree can be seen as special cases of central forests in trees. A central…