Related papers: Weight systems and invariants of graphs and embedd…
In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: 1) quantum group invariants using the R-matrix, 2) the Kontsevich universal link invariant followed by the Lie algebra…
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…
This work explores areas overlapping music, graph theory, and machine learning. An embedding representation of a node, in a weighted undirected graph $\mathcal{G}$, is a representation that captures the meaning of nodes in an embedding…
We study the properties of several proximity measures for the vertices of weighted multigraphs and multidigraphs. Unlike the classical distance for the vertices of connected graphs, these proximity measures are applicable to weighted…
We show that embedding calculus invariants $ev_n$ are surjective for long knots in an arbitrary $3$-manifold. This solves some remaining open cases of Goodwillie--Klein--Weiss connectivity estimates, and at the same time confirms one half…
This paper proposes a new method for converting a time-series into a weighted graph (complex network), which builds on the electrostatic conceptualization originating from physics. The proposed method conceptualizes a time-series as a…
The concept of diagrammatic combinatorial Hopf algebras in the form introduced for describing the Heisenberg-Weyl algebra in~\cite{blasiak2010combinatorial} is extended to the case of so-called rule diagrams that present graph rewriting…
Chord diagrams and related enlacement graphs of alternating knots are enhanced to obtain complete invariant graphs including chirality detection. Moreover, the equivalence by common enlacement graph is specified and the neighborhood graph…
We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric…
We describe a correspondence between GL_n-invariant tensors and graphs, and show how this correspondence accomodates various types of symmetries and orientations.
Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph…
This paper deals with spectral graph theory issues related to questions of monotonicity and comparison of eigenvalues. We consider finite directed graphs with non symmetric edge weights and we introduce a special self-adjoint operator as…
This paper aims to develop a mathematical foundation to model knitting with graphs. We provide a precise definition for knit objects with a knot theoretic component and propose a simple undirected graph, a simple directed graph, and a…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…