Related papers: Dynamic Generators of Topologically Embedded Graph…

The recent deep generative models for static graphs that are now being actively developed have achieved significant success in areas such as molecule design. However, many real-world problems involve temporal graphs whose topology and…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…

Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction…

Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…

With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\Omega(\log n)$ update/query time.…

We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report…

This chapter provides a comprehensive survey of foundational results and recent advances concerning minimal generating sets for the mapping class group of a nonorientable surface, $\mathrm{Mod}(N_{g})$, and its index-two twist subgroup,…

A tensor network is a product of tensors associated with vertices of some graph $G$ such that every edge of $G$ represents a summation (contraction) over a matching pair of indexes. It was shown recently by Valiant, Cai, and Choudhary that…

Neural networks for structured data like graphs have been studied extensively in recent years. To date, the bulk of research activity has focused mainly on static graphs. However, most real-world networks are dynamic since their topology…

Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various…

The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel…

A minimal separating set in a connected topological space $X$ is a subset $L \subset X$ with the property that $X \setminus L$ is disconnected, but if $L^{\prime}$ is a proper subset of $L$, then $X \setminus L^{\prime}$ is connected. Such…

Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…

Indyk and Sidiropoulos (2007) proved that any orientable graph of genus $g$ can be probabilistically embedded into a graph of genus $g-1$ with constant distortion. Viewing a graph of genus $g$ as embedded on the surface of a sphere with $g$…

In this paper, we give new, tight subexponential lower bounds for a number of graph embedding problems. We introduce two related combinatorial problems, which we call String Crafting and Orthogonal Vector crafting, and show that these…

Are the embeddings of a graph's degenerate core stable? What happens to the embeddings of nodes in the degenerate core as we systematically remove periphery nodes (by repeated peeling off $k$-cores)? We discover three patterns w.r.t.…

With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…

In this paper, we address the problem of enumerating all induced subtrees in an input k-degenerate graph, where an induced subtree is an acyclic and connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for any its…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. Recent work at the intersection of formal language theory and graph theory has found that a Hyperedge Replacement Grammar (HRG)…