arXiv research

Existence and uniqueness theorem for Ricci flow on weighted graphs proved.

Constructs graph manifolds with many Anosov flows.

New method shows pseudo-Anosov flows on graph manifolds can be simplified.

New curvature defined via graph resistances leads to Ricci flow.

The paper explores heat flow and constants on graphs, proving properties and proposing new concepts.

Graph neural network using Beltrami flow for feature and topology evolution.

Study of mean curvature flows on graphs in warped product manifolds, focusing on behavior at infinity.

New Ricci flow method for directed graphs with balancing factor.

In this paper, following J. Franks' work on Lyapunov graphs of nonsingular Smale flows on $S^3$, we study Lyapunov graphs of nonsingular Smale flows on $S^1 \times S^2$. More precisely, we determine necessary and sufficient conditions on an abstract Lyapunov graph to be associated with a nonsingular Smale flow on $S^1 …

Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly reduced memory footprint, allowing them to scale to larger graphs. In the unsupervis…

The paper introduces a new type of Ricci flow on graphs to study their curvature.

Graph Ricci flow reveals hidden hierarchies in stock market correlations.

Study on planar graphs in Poincare model of hyperbolic geometry.

Flow preserves curvature sharpness on weighted graphs.

Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…

We present a notion of super Ricci flow for time-dependent finite weighted graphs. A challenging feature is that these flows typically encounter singularities where the underlying graph structure changes. Our notion is robust enough to allow the flow to continue past these singularities. As a crucial tool for this purp…

Proposes a new model for traffic flow on directed graphs.

Shapley Flow interprets model predictions using a graph-based approach to feature importance.

Graph neural networks are explained through energy gradient flow and framelet decomposition.

Classifies solitons for surface diffusion flow of graphs.

We present a graph-based semi-supervised learning (SSL) method for learning edge flows defined on a graph. Specifically, given flow measurements on a subset of edges, we want to predict the flows on the remaining edges. To this end, we develop a computational framework that imposes certain constraints on the overall fl…

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that …

Flow on weighted graphs sharpens Bakry-Émery curvature.

We present two initial graphs over the entire $\mathbb{R}^n$, $n \geq 2$ for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flows stabilize at different heights. With our second example, the mean curvature flow oscillates indefinitely while the heat flow stabilizes. …

The Ollivier Ricci flow with prescribed curvature on infinite graphs.

Study on veering triangulations and their flow graphs, proving new applications.

GC-Flow uses graph flows for better clustering than traditional GCNs.

The paper solves curvature problems on graphs using a special flow.

MoFlow generates chemically valid molecular graphs from latent representations.

We consider the $Q_k$ flow on complete non-compact graphs. We prove that a complete graph evolves by the $Q_k$ curvature up to some time $T$ depending on the radius of a sphere enclosed by the initial graph.

Generative Flow Networks solve shortest path problems in graphs.

CatFlow uses variational flow matching for efficient graph generation.

We propose GraphNVP, the first invertible, normalizing flow-based molecular graph generation model. We decompose the generation of a graph into two steps: generation of (i) an adjacency tensor and (ii) node attributes. This decomposition yields the exact likelihood maximization on graph-structured data, combined with t…

One fundamental issue in managing bike sharing systems is the bike flow prediction. Due to the hardness of predicting the flow for a single station, recent research works often predict the bike flow at cluster-level. While such studies gain satisfactory prediction accuracy, they cannot directly guide some fine-grained …

Study connects flow dynamics to 3D geometry via surface intersections.

In this note we study a large class of mean curvature type flows of graphs in product manifold $N\times R$ where N is a closed Riemann- ian manifold. Their speeds are the mean curvature of graphs plus a prescribed function. We establish long time existence and uniformly convergence of those flows with a barrier conditi…

The study characterizes heat flow and concentration on directed graphs with a lower Ricci curvature bound.

Symmetric graphs flow without singularities on their axis.

We study a Neumann problem related to the evolution of graphs under mean curvature flow in Riemannian manifolds endowed with a Killing vector field. We prove that in a particular case these graphs converge to a bounded minimal graph which contacts the cylinder over the domain orthogonally along its boundary.

We show that the metric of nonpositively curved graph manifolds is determined by its geodesic flow. More precisely we show that if the geodesic flows of two nonpositively curved graph manifolds are $C^0$ conjugate then the spaces are isometric.

In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally provides a detailed, transparent, and easily understood expression of the learn…

The paper proves uniqueness of evolving graphs by mean curvature flow under specific conditions.

The paper studies curve shortening flows on non-convex surfaces.

DIGRAC clusters directed graphs using flow imbalance, outperforming existing methods.

In this work we study the geodesic flow on nilmanifolds associated to graphs. We are interested in the construction of first integrals to show complete integrability on some compact quotients. Also examples of integrable geodesic flows and of non-integrable ones are shown.

The aim of this work is studying translating graphs by mean curvature flow in $\Real^3$. We prove non-existence of complete translating graphs over bounded domains in $\Real^2$. Furthermore, we show that there are only three types of complete translating graphs in $\Real^3$; entire graphs, graphs between two vertical p…

Let $M$ be a complete Riemannian manifold which either is compact or has a pole, and let $\varphi$ be a positive smooth function on $M$. In the warped product $M\times_\varphi\mathbb R$, we study the flow by the mean curvature of a locally Lipschitz continuous graph on $M$ and prove that the flow exists for all time an…