Related papers: Shattering, Graph Orientations, and Connectivity
Urban mobility forecast and analysis can be addressed through grid-based and graph-based models. However, graph-based representations have the advantage of more realistically depicting the mobility networks and being more robust since they…
Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…
We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite…
The vertex connectivity of a graph $G$ is the size of the smallest set of vertices $S$ such that $G \setminus S$ is disconnected. For the class of planar graphs, the problem of vertex connectivity is well-studied, both from structural and…
Over all graphs (or unicyclic graphs) of a given order, we characterise those graphs that minimise or maximise the number of connected induced subgraphs. For each of these classes, we find that the graphs that minimise the number of…
In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of…
Graph representation learning models aim to represent the graph structure and its features into low-dimensional vectors in a latent space, which can benefit various downstream tasks, such as node classification and link prediction. Due to…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
As is well known, a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Therefore, it is not surprising that many of the first results concerning graphs made reference to…
The eccentric connectivity index of a graph $G$, denoted by $\xi^{c}(G)$, defined as $\xi^{c}(G)$ = $\sum_{v \in V(G)}\epsilon(v) \cdot d(v)$, where $\epsilon(v)$ and $d(v)$ denotes the eccentricity and degree of a vertex $v$ in a graph…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus,…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
The principal ratio of a graph is the ratio of the greatest and least entry of its principal eigenvector. Since the principal ratio compares the extreme values of the principal eigenvector it is sensitive to outliers. This can be…
Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
We generalize theorems of Kesten and Deuschel-Pisztora about the connectedness of the exterior boundary of a connected subset of $\mathbb{Z}^d$, where "connectedness" and "boundary" are understood with respect to various graphs on the…