arXiv research

In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graph partitions. The two types of measures, graph-aware and set parti…

Study recovers community structure from coarse graph measurements.

Study graph products of groups, classifying them up to measure equivalence and rigidity.

As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures rely on the assumption that the graph is perfectly known -- a premise …

This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topog…

We extend Sobolev transport to unbalanced measures on graphs.

Study shows SNN graph Laplacians converge to k-NN graph Laplacians under large scale asymptotics.

Measure-scaling quasi-isometries on graphs have specific scaling groups.

Graph neural networks improve with affinity measures from random walks.

New measures assess differences in causal graphs' separations.

The paper defines surface area for graphs and derives spectral estimates.

A novel approach to computing barycenters on graph-supported probability measures.

We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of "hyperbolic measures" on universal covers of metric graphs. Kazhdan's theorem for Riemann surfaces describes the limiting behavior of canonical (Arakelov) measures on finite covers in rela…

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows us to derive an explicit expression of the Wasserstein distance between graph s…

The study learns causal graphs from time series data using entropy measures.

In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the perturbation cannot be well controlled. We firstly provide a perturbation framework on …

Critical graphs of quadratic differentials equidistribute in moduli space.

Right-angled Artin groups are classified based on measure equivalence.

Estimates smooth graph signals from partial measurements.

Novel algorithm speeds up computation of Sobolev IPM for graph-based probability measures.

New method synchronizes graphs with probability measures on rotations.

Implementing $k$-NN classification using Gromov--Wasserstein distances

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

Few-shot graph classification on graphs with limited labeled examples.

Proposes methods for local clustering in attributed graphs.

A new metric for comparing probability measures on graphs, scalable and negative definite.

Hyperbolic groups' infinite orbits spread evenly in spaces.

We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponen…

We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if the action is expanding in measure. This provides a somewhat unified approach to construct expanders. We also show that the graphs we obtain …

New graph invariant measures embeddability in 3D.

For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The measure is intuitive given the abnormal samples are usually rare and they are dissi…

We use multiple measures of graph complexity to evaluate the realism of synthetically-generated networks of human activity, in comparison with several stylized network models as well as a collection of empirical networks from the literature. The synthetic networks are generated by integrating data about human populatio…

This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian distributions that factorize with respect to a chain graph $G$ with $d$ parameters have positive Lebesgue measure with respect to $\mathbb{R}^d$, whereas those that factorize with respect…

Graph neural networks improve systemic risk measures for financial networks.

A new method for transporting unbalanced measures on graphs efficiently.

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

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…

The paper confirms a conjecture linking link bipyramid volume and Mahler measure.

This paper is concerned with jointly recovering $n$ node-variables $\left\{ x_{i}\right\}_{1\leq i\leq n}$ from a collection of pairwise difference measurements. Imagine we acquire a few observations taking the form of $x_{i}-x_{j}$; the observation pattern is represented by a measurement graph $\mathcal{G}$ with an ed…

Study area and coarea formulas for graphs and submanifolds in Carnot groups.

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $ΔG$ of the graph and try to improve generalization. Based on quantum information geometry, $ΔG$ can be characterized by the eigendecomposition of the graph Laplaci…

This paper examines properties of feedforward graphs to improve neural network performance.

Improved graph neural network bounds using graph diffusion matrix.

Assessing generative models is not an easy task. Generative models should synthesize graphs which are not replicates of real networks but show topological features similar to real graphs. We introduce an approach for assessing graph generative models using graph classifiers. The inability of an established graph classi…

Identifies directed graphs from node measurements using polynomial filters.

Unified geometric scattering model for measure spaces.

Uniform drift estimates found for random walks on graph products.

New curvature measure defined for graphs, with bounds on diameter and spectral gap.