arXiv research

Generative model captures hubs and dense communities in social networks.

The paper explores graphons of line graphs from sparse finite graphs.

The paper classifies dense conjugacy classes in mapping class groups of locally finite graphs.

Paper tackles dense subgraph discovery with noisy feedback.

The paper bounds crossing numbers of dense graphs on surfaces.

A new algorithm reduces graph complexity for better dense subgraph analysis.

Study on detecting and recovering hidden dense cycles in random graphs.

SpaPool combines dense and sparse techniques for efficient graph pooling.

Detection of dense cycles in graphs reveals a gap between easy detection and hard recovery.

Polynomial-time test for detecting dense subgraphs in heterogeneous networks.

New tests detect communities in dense bipartite graphs with high accuracy.

Dense neural networks can't approximate all functions.

Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining \cite{Duda,Mishra}. Recently, Ames and Vavasis have suggested a novel method for finding cliques i…

Hyperbolic groups' infinite orbits spread evenly in spaces.

A new GCN variant tackles large eigengaps in dense graphs and hypergraphs.

New solver MPLP++ outperforms existing solvers for dense graph models.

We analyze the sample complexity of learning graphical games from purely behavioral data. We assume that we can only observe the players' joint actions and not their payoffs. We analyze the sufficient and necessary number of samples for the correct recovery of the set of pure-strategy Nash equilibria (PSNE) of the true…

Graph neural networks have become increasingly popular in recent years due to their ability to naturally encode relational input data and their ability to scale to large graphs by operating on a sparse representation of graph adjacency matrices. As we look to scale up these models using custom hardware, a natural assum…

We survey the construction and properties of the Yamada polynomial of spatial graphs and present the Yamada polynomial formulae for some classes of graphs. Then we construct an infinite family of spatial graphs for which roots of Yamada polynomials are dense in the complex plane.

Sharp boundaries for detecting dense subhypergraphs established.

Chromatic Learning reduces feature dimensions for sparse datasets.

Detects dense subhypergraphs in random hypergraphs using low-degree polynomials.

This paper studies the problem of detecting the presence of a small dense community planted in a large Erdős-Rényi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor. Assuming the hardness of the planted clique detection problem, we show that the computatio…

We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in …

We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erdős-Rényi random graphs, with an initial seed set of correctly matched vertex pairs revealed as side information. For seeded problems, our result pr…

New neural model processes 2D data with long-range dependencies efficiently.

Study on stable translation lengths of surface homeomorphisms and their approximations.

Sparse sampling method for tensor factorization and completion of high rank tensors.

We focus on developing a novel scalable graph-based semi-supervised learning (SSL) method for a small number of labeled data and a large amount of unlabeled data. Due to the lack of labeled data and the availability of large-scale unlabeled data, existing SSL methods usually encounter either suboptimal performance beca…

We propose a new graph kernel for graph classification and comparison using Ollivier Ricci curvature. The Ricci curvature of an edge in a graph describes the connectivity in the local neighborhood. An edge in a densely connected neighborhood has positive curvature and an edge serving as a local bridge has negative curv…

This short note aims at (re)proving that the symmetrically normalized graph Laplacian $L=\Id - D^{-1/2}WD^{-1/2}$ (from a graph defined from a Gaussian weighting kernel on a sampled smooth manifold) converges towards the continuous Manifold Laplacian when the sampling become infinitely dense. The convergence rate with …

DiPhon generates scalable graphs via diffusion on graphons.

Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploi…

We introduce and study the operation, called dense amalgam, which to any tuple X_1,...,X_k of non-empty compact metric spaces associates some disconnected perfect compact metric space, denoted $\widetilde\sqcup(X_1,...,X_k)$, in which there are many appropriately distributed copies of the spaces X_1,...,X_k. We then sh…

Researchers describe the Gromov boundary of a graph related to surfaces.

Brooks and Makover introduced an approach to random Riemann surfaces based on associating a dense set of them - Belyi surfaces - with random cubic graphs. In this paper, using Bollobas model for random regular graphs, we examine the topological structure of these surfaces, obtaining in particular an estimate for the ex…

This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain a large amount of low-cost trees with high outdegrees while low-density regions…

The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes computations, in particular matrix-vector products, with the graph Laplacian a ha…

New algorithms reduce communication in GNN training.

The effectiveness of Graph Convolutional Networks (GCNs) has been demonstrated in a wide range of graph-based machine learning tasks. However, the update of parameters in GCNs is only from labeled nodes, lacking the utilization of unlabeled data. In this paper, we apply Virtual Adversarial Training (VAT), an adversaria…

Real-time traffic volume inference is key to an intelligent city. It is a challenging task because accurate traffic volumes on the roads can only be measured at certain locations where sensors are installed. Moreover, the traffic evolves over time due to the influences of weather, events, holidays, etc. Existing soluti…

For $0\leq H< 1/2$, we construct entire $H$-graphs in $\mathbb{H}^2\times\mathbb{R}$ that are parabolic and not invariant by one parameter groups of isometries of $\mathbb{H}^2\times\mathbb{R}$. Their asymptotic boundaries are $(\partial_\infty\mathbb{H}^2)\times\mathbb{R}$; they are dense at infinity. When $H=0$ the e…

Paper tackles robust graph matching in dense graphs with AMP type algorithm.

In this paper, we present a general framework to scale graph autoencoders (AE) and graph variational autoencoders (VAE). This framework leverages graph degeneracy concepts to train models only from a dense subset of nodes instead of using the entire graph. Together with a simple yet effective propagation mechanism, our…

Spectral algorithms solve optimal community detection and related problems.

While sparse inverse covariance matrices are very popular for modeling network connectivity, the value of the dense solution is often overlooked. In fact the L2-regularized solution has deep connections to a number of important applications to spectral graph theory, dimensionality reduction, and uncertainty quantificat…

Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is necessarily either dens…

We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The n-th subgraph of this family is generated by all knots whose fundamental groups surject to a symmetric group with parameter at least n, where all meridians are mapped to transpositions. Incidentally, we verify the Meridio…