Related papers: Ordered Exchange Graphs
We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…
Combinatorial Hopf algebras of trees exemplify the connections between operads and bialgebras. Painted trees were introduced recently as examples of how graded Hopf operads can bequeath Hopf structures upon compositions of coalgebras. We…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
Circuit algebras are a symmetric analogue of Jones's planar algebras introduced to study finite-type invariants of virtual knotted objects. Circuit algebra structures appear, in different forms, across mathematics. This paper provides a…
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers' which are oriented hypergraphs. We describe mutations of such…
We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Graph clustering, aiming to partition nodes of a graph into various groups via an unsupervised approach, is an attractive topic in recent years. To improve the representative ability, several graph auto-encoder (GAE) models, which are based…
This is the first one of a series of papers on association of orientations, lattice polytopes, and abelian group arrangements to graphs. The purpose is to interpret the integral and modular tension polynomials of graphs at zero and negative…
We develop a general diagrammatic theory of welded graphs, and provide an extension of Satoh's Tube map from welded graphs to ribbon surface-links. As a topological application, we obtain a complete link-homotopy classification of so-called…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. In this…
Let $\Delta$ be an oriented valued graph equipped with a group of admissible automorphisms satisfying a certain stability condition. We prove that the (coefficient-free) cluster algebra $\mathcal A(\Delta/G)$ associated to the valued…
Exponential random graph theory is the complex network analog of the canonical ensemble theory from statistical physics. While it has been particularly successful in modeling networks with specified degree distributions, a naive model of a…
Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured,…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…