Related papers: A Graph Theoretic Analysis of Leverage Centrality
We introduce novel measures, L1 prestige and L1 centrality, for quantifying the prominence of each vertex in a strongly connected and directed graph by utilizing the concept of L1 data depth (Vardi and Zhang, Proc. Natl. Acad. Sci. U.S.A.\…
In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
Community and core-periphery are two widely studied graph structures, with their coexistence observed in real-world graphs (Rombach, Porter, Fowler \& Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]). However, the nature of this…
Complex network theory (CNT) is gaining a lot of attention in the scientific community, due to its capability to model and interpret an impressive number of natural and anthropic phenomena. One of the most active CNT field concerns the…
We consider the generalised friendship paradox, focussing on the number of triangles at a vertex as the relevant attribute. We show that, contrary to the setting where the attribute is the number of edges at a vertex or the number of wedges…
In general graph theory, the only relationship between vertices are expressed via the edges. When the vertices are embedded in an Euclidean space, the geometric relationships between vertices and edges can be interesting objects of study.…
Deep, classical graph-theoretical parameters, like the size of the minimum vertex cover, the chromatic number, or the eigengap of the adjacency matrix of the graph were studied widely by mathematicians in the last century. Most researchers…
The Divisibility Graph of a finite group $G$ has vertex set the set of conjugacy class lengths of non-central elements in $G$ and two vertices are connected by an edge if one divides the other. We determine the connected components of the…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
We present a new metric of link cohesion for measuring the strength of edges in complex, highly connected graphs. Link cohesion accounts for local small hop connections and associated node degrees and can be used to support edge scoring and…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
For decades, researchers in information visualisation and graph drawing have focused on developing techniques for the layout and display of very large and complex networks. Experiments involving human participants have also explored the…
Graph embedding techniques allow to learn high-quality feature vectors from graph structures and are useful in a variety of tasks, from node classification to clustering. Existing approaches have only focused on learning feature vectors for…