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Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
In designing and applying graph neural networks, we often fall into some optimization pitfalls, the most deceptive of which is that we can only build a deep model by solving over-smoothing. The fundamental reason is that we do not…
We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…
In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially…
We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the ob- servation of smaller graphs and basic structure of our heuristics.…
We study the problem of embedding graphs in the plane as good geometric spanners. That is, for a graph $G$, the goal is to construct a straight-line drawing $\Gamma$ of $G$ in the plane such that, for any two vertices $u$ and $v$ of $G$,…
The $k$-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct $k$-NN graphs remains a challenge, especially for…
In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly $90^\circ$, where the number of bends on such polylines is typically restricted in some way.…
In the past decades, many graph drawing techniques have been proposed for generating aesthetically pleasing graph layouts. However, it remains a challenging task since different layout methods tend to highlight different characteristics of…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…
A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is…
Both Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms. This contrast is evident in Multidimensional Scaling (MDS), which typically depends on…
We propose data-driven one-pass streaming algorithms for estimating the number of triangles and four cycles, two fundamental problems in graph analytics that are widely studied in the graph data stream literature. Recently, (Hsu 2018) and…
Graphs, consisting of vertices and edges, are vital for representing complex relationships in fields like social networks, finance, and blockchain. Visualizing these graphs helps analysts identify structural patterns, with readability…
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
Unit edge-length drawings, rectilinear drawings (where each edge is either a horizontal or a vertical segment), and rectangular face drawings are among the most studied subjects in Graph Drawing. However, most of the literature on these…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…
We address the problem of constructing large undirected circulant networks with given degree and diameter. First we discuss the theoretical upper bounds and their asymptotics, and then we describe and implement a computer-based method to…