Related papers: Metric spaces and sparse graphs
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…
Given a connected graph $G$, the metric (resp. edge metric) dimension of $G$ is the cardinality of the smallest ordered set of vertices that uniquely identifies every pair of distinct vertices (resp. edges) of $G$ by means of distance…
Given a dense countable set in a metric space, the infinite random geometric graph is the random graph with the given vertex set and where any two points at distance less than 1 are connected, independently, with some fixed probability. It…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
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…
We introduce the {\em pair-cut cone $PCUT_n$} of metrics on sets with $n\ge 3$ elements, that correspond to linear combinations with non-negative coefficients of the cut-metrics resulting from cuts that are pairs. Given a metric, we fully…
We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter provides a…
A metric graph is a 1-dimensional stratified metric space consisting of vertices and edges or loops glued together. Metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as…
In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by…
In 2007 H. Long-Guang and Z. Xian, [H. Long-Guang and Z. Xian, Cone Metric Spaces and Fixed Point Theorems of Contractive Mapping, J. Math. Anal. Appl., 322(2007), 1468-1476], generalized the concept of a metric space, by introducing cone…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vessels, and filamentary structures in galaxies. To study metric…
The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…
We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
We investigate how the metric dimension of infinite graphs change when we add edges to the graph. Our two main results: (1) there exists a growing sequence of graphs (under the subgraph relation, but without adding vertices) for which the…
S-metric and b-metric spaces are metrizable, but it is still quite impossible to get an explicit form of the concerned metric function. To overcome this, the notion of $\phi$-metric is developed by making a suitable modification in triangle…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
We study the metric dimension (strong and weak) of infinite graphs. In particular, our main interest is characterizing infinite graphs with finite dimension. Our main results: (1) graphs with more than one end have infinite strong…