arXiv research

The study finds conditions on graph complements for positive curvature.

Study lens spaces' definite fillings, classifying those with specific inequalities.

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank \cite{Frank1978} of estimating the number of connected components in a large graph based …

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the {\it forbidden number}. We relate the forbidden number to several known invarian…

Forbidden moves categorify fused links into quivers.

We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group $A(K)$ has such a subgroup if its defining graph $K$ contains an $n$-hole (i.e. an induced cycle of length $n$) with $n\geq 5$. We construct another eight "forbidden" grap…

We show that the forbidden detour move, essentially introduced by Kanenobu and Nelson, is an unknotting operation for virtual knots. Then we define the forbidden detour number of a virtual knot to be the minimal number of forbidden detour moves necessary to transform a diagram of the virtual knot into the trivial knot …

This paper classifies minimal fillings of lens spaces.

New moves help untangle complex knots.

The existence of forbidden patterns, i.e., certain missing sequences in a given time series, is a recently proposed instrument of potential application in the study of time series. Forbidden patterns are related to the permutation entropy, which has the basic properties of classic chaos indicators, thus allowing to sep…

The forbidden moves can be combined with Gauss diagram Reidemeister moves to obtain move sequences with which we may change any Gauss diagram (and hence any virtual knot) into any other, including in particular the unknotted diagram

32 knot projections classified based on forbidden Reidemeister moves.

SubGNN tackles subgraph prediction challenges in graphs.

Certain research strands can yield "forbidden knowledge". This term refers to knowledge that is considered too sensitive, dangerous or taboo to be produced or shared. Discourses about such publication restrictions are already entrenched in scientific fields like IT security, synthetic biology or nuclear physics researc…

The paper introduces subgraph nomination for finding similar subgraphs in networks.

NeuroMatch efficiently matches subgraphs in large graphs using neural networks.

Unified framework for subgraph-enhanced GNNs, improving prediction accuracy and reducing computation time.

Study area-minimizing subgraphs in integer lattices.

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by …

GNNS uses graph neural networks to efficiently estimate subgraph frequency distributions.

Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here we investigate the relation between knotoids differing only by small perturbations of the direc…

Proposes GIB for recognizing informative subgraphs in graphs.

The H(n)-move simplifies virtual and welded knots and links.

We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We propose a new convex relaxation for the densest $k$-subgraph problem, based on a nucle…

RevTrack identifies suspicious subgraphs on blockchain for AML.

Faster algorithm for generalized mean densest subgraph problem.

Let $Γ$ be a finite graph and let $Γ^{\mathrm{e}}$ be its extension graph. We inductively define a sequence $\{Γ_i\}$ of finite induced subgraphs of $Γ^{\mathrm{e}}$ through successive applications of an operation called "doubling along a star". Then we show that every finite induced subgraph of $Γ^{\mathrm{e}}$ is iso…

Classification and regression in which the inputs are graphs of arbitrary size and shape have been paid attention in various fields such as computational chemistry and bioinformatics. Subgraph indicators are often used as the most fundamental features, but the number of possible subgraph patterns are intractably large …

The inertia subgroup $I_n(π)$ of a surgery obstruction group $L_n(π)$ is generated by elements which act trivially on the set of homotopy triangulations $\Cal S(X)$ for some closed topological manifold $X^{n-1}$ with $π_1(X)=π$. This group is a subgroup of the group $C_n(π)$ which consists of the elements which can be …

Mining discriminative subgraph patterns from graph data has attracted great interest in recent years. It has a wide variety of applications in disease diagnosis, neuroimaging, etc. Most research on subgraph mining focuses on the graph representation alone. However, in many real-world applications, the side information …

Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.

Efficiently matches subgraphs in noisy data without node labels.

ESAN improves graph neural networks by processing subgraphs.

Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interestingness of discriminative subgraph features are defined on certain graphs, where the structure of graph objec…

We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin diagrams, as well as a simple classification of alternating positive braid knots.

In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it …

We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, …

Upper bounds for Steklov eigenvalues in subgraphs of polynomial growth Cayley graphs.

GMT improves interpretability of XGNNs by approximating SubMT.

Introduces a new manifold from a graph subgraph.

SELO model predicts link signs better than SDGNN using subgraph encoding and linear optimization.

Neural network for subgraph similarity computation with pruning.

PSimGNN partitions graphs into subgraphs for efficient graph similarity computation.

Metric graphs have subgraphs with entropy at least λ.

The study extends Tutte's conflict graph concept to nonplanar graphs.

Finite subgraphs in flip graphs ensure unique surface embeddings.

We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.

Cohomology defines hyperbolic spaces and their subgraphs.