Related papers: Local Routing in Graphs Embedded on Surfaces of Ar…
Graph Neural Networks (GNNs) have received increasing attention for representation learning in various machine learning tasks. However, most existing GNNs applying neighborhood aggregation usually perform poorly on the graph with…
It has been recently shown that any graph of genus g>0 can be stochastically embedded into a distribution over planar graphs, with distortion Olog (g+1)) [Sidiropoulos, FOCS 2010]. This embedding can be computed in polynomial time, provided…
Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…
Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require…
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…
For a given spatial graph $\mathcal{G} \subset \mathbb{R}^3$, we would like to find a closed orientable surface $\mathcal{S}$ embedded in $\mathbb{R}^3$ in which $\mathcal{G}$ is cellular embedded. However, for general $\mathcal{G}$ this is…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…
Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…
Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive…
We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels…
The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…
For graphs $G$ and $H$, a homomorphism from $G$ to $H$ is a function $\varphi \colon V(G) \to V(H)$, which maps vertices adjacent in $G$ to adjacent vertices of $H$. A homomorphism is locally injective if no two vertices with a common…
Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
We prove that given any $\alpha$-approximation LOCAL algorithm for Minimum Dominating Set (MDS) on planar graphs, we can construct an $f(g)$-round $(3\alpha+1)$-approximation LOCAL algorithm for MDS on graphs embeddable in a given Euler…