arXiv research

New relations for vertex polynomial in graphs of any degree.

A distributed Nesterov method for arbitrary graphs achieves faster convergence.

New forms calibrate minimal graphs in arbitrary dimensions.

We prove that a graph is intrinsically linked in an arbitrary 3-manifold M if and only if it is intrinsically linked in S^3. Also, assuming the Poincare Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S^3.

The conformal invariance and universality results of Chelkak-Smirnov on the two-dimensional Ising model hold for isoradial planar graphs with critical weights. Motivated by the problem of extending these results to a wider class of graphs, we define a generalized notion of s-holomorphicity for functions on arbitrary we…

A graph product kernel means the kernel of the natural surjection from a graph product to the corresponding direct product. We prove that a graph product kernel of countable groups is special, and a graph product of finite or cyclic groups is virtually cocompact special in the sense of Haglund and Wise. The proof of th…

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtai…

The paper explores weight systems and their applications to graph and embedded graph invariants.

We characterize which automorphisms of an arbitrary complete bipartite graph $K_{n,m}$ can be induced by a homeomorphism of some embedding of the graph in $S^3$.

iPool selects informative nodes for pooling in arbitrary graphs.

Graphs derived from cohomology help reconstruct defining graphs of Artin groups.

This paper studies rectifiability in Carnot groups and proves geometric area formulas.

We obtain a Bernstein theorem for special Lagrangian graphs in n-dimensional complex space for arbitrary n only assuming bounded slope, but no quantitative restriction.

Graphon autoencoder generates graphs with arbitrary sizes using Chebyshev filters.

Previous work in network analysis has focused on modeling the mixed-memberships of node roles in the graph, but not the roles of edges. We introduce the edge role discovery problem and present a generalizable framework for learning and extracting edge roles from arbitrary graphs automatically. Furthermore, while existi…

We embed arbitrary groups into regular graphs with prescribed automorphisms.

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful new approach for learning generative models over graphs, which can capture both …

For each commutative, graded algebra with finite dimension in each degree, we construct a graded cohomology theory for graphs whose graded Euler characteristic is the chromatic polynomial of the graph. This extends our previous work which was based on the algebra $\mathbb {Z}[x]/(x^2)$.

We study the Dirichlet problem for minimal surface systems in arbitrary dimension and codimension via mean curvature flow, and obtain the existence of minimal graphs over arbitrary mean convex bounded $C^2$ domains for a large class of prescribed boundary data. This result can be seen as a natural generalization of the…

We calculate the intersection ring of three-dimensional graph manifolds with rational coefficients and give an algebraic characterization of these rings when the manifold's underlying graph is a tree. We are able to use this characterization to show that the intersection ring obstructs arbitrary three-manifolds from be…

Simplified identification methods for causal inference with arbitrary interventional distributions.

New graph learning model can approximate any function and handle edge values.

The paper generalizes linking number properties for complete graphs.

This paper is first-line research expanding GANs into graph topology analysis. By leveraging the hierarchical connectivity structure of a graph, we have demonstrated that generative adversarial networks (GANs) can successfully capture topological features of any arbitrary graph, and rank edge sets by different stages a…

We consider immersions admitting uniform representations as an L-Lipschitz graph. In codimension 1, we show compactness for such immersions for arbitrary fixed finite L and uniformly bounded volume. The same result is shown in arbitrary codimension for L less than or equal to 1/4.

The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The corresponding Cardy-Frobenius algebra is induced by arbitrary Young diagrams and …

This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transit…

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and con…

We find families of prime knot diagrams with arbitrary extreme coefficients in their Jones polynomials. Some graph theory is presented in connection with this problem, generalizing ideas by Yongju Bae and Morton and giving a positive answer to a question in their paper.

New methods predict drug interactions using drug co-medication patterns and graph matching.

Generates low-dimensional node vectors for graphs with privacy while preserving structural preferences.

We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of…

We study the problem of finding a minimal graph with prescribed boundary data in arbitrary dimension and codimension. Existence, uniqueness, stability and regularity are treated. We first present the well-known results for codimension one: Jenkins-Serrin's existence theorem, convexity properties of the area which give …

The paper calculates asymptotic Betti numbers and homology multiplicities for graph configuration spaces.

We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary graphs of groups, we show that if their fundamental group is not one-ended, then we can blow up vertex groups to graphs of groups with simp…

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that op…

We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We sho…

Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are d…

A strong interaction is known to exist between edge-colored graphs (which encode PL pseudo-manifolds of arbitrary dimension) and random tensor models (as a possible approach to the study of Quantum Gravity). The key tool is the {\it G-degree} of the involved graphs, which drives the {\it $1/N$ expansion} in the tensor …

We consider the group of isotopy classes of automorphisms of the 3-sphere that preserve a spatial graph or a handlebody-knot embedded in it. We prove that the group is finitely presented for an arbitrary spatial graph or a reducible handlebody-knot of genus two. We also prove that the groups for "most" irreducible genu…

The study bounds the effective diameter of graphs with positive Ollivier curvature.

The study combines graph-minors and metric spaces, answering some questions and conjectures.

This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all have free fundamental group).

Unified deep learning for graph signals, simplifying existing models.

This paper discusses reformulations of the problem of coloring plane maps with four colors. We give a number of alternate ways to formulate the coloring problem including a tautological expansion similar to the Penrose Bracket, and an extension of the Penrose Bracket that counts colorings of arbitrary cubic graphs pres…

Efficient memory layer improves graph neural networks for graph classification and regression.

GNPs use graph neural networks to predict target points with uncertainty quantification.

This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This impli…