In [1], a new construction called red-black hierarchy characterizing Laman graphs and an algorithm for computing it were presented. For a Laman graph G = (V,E) with n vertices it runs in O(n) time assuming that a partition of G + e, e ∈ E into two spanning trees is given. We show that a simple modification reduces the running time to O(n log n). The total running time can be reduced O(n √ n log...

We propose a new graph layout method based on a modification of the t-distributed Stochastic Neighbor Embedding (t-SNE) dimensionality reduction technique. Although t-SNE is one of the best techniques for visualizing high-dimensional data as 2D scatterplots, t-SNE has not been used in the context of classical graph layout. We propose a new graph layout method, tsNET, based on representing a gra...

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎

In this article we examine four objections to the genetic modification of human beings: the freedom argument, the giftedness argument, the authenticity argument, and the uniqueness argument. We then demonstrate that each of these arguments against genetic modification assumes a strong version of genetic determinism. Since these strong deterministic assumptions are false, the arguments against g...

We describe the Scene-Graph-As-Bus technique (SGAB), the first step in a staircase of solutions for sharing software components for virtual environments. The goals of SGAB are to allow, with minimal effort, independentlydesigned applications to share component functionality; and for multiple users to share applications designed for single users. This paper reports on the SGAB design for transpa...

Link prediction, the problem of identifying missing links among a set of inter-related data entities, is a popular field of research due to its application to graph-like domains. Producing consistent evaluations of the performance of the many link prediction algorithms being proposed can be challenging due to variable graph properties, such as size and density. In this paper we first discuss tr...

Given: (a) clean training dataset, (b) trained graph machine learning pipeline, and (c) noisy test dataset; how do we make the pipeline robust to such noise? In an attempt answer this question, propose a modification that exploits both content addressability of restricted Boltzmann message passing capabilities neural network. We investigate which hidden layers is best suited for our proposed mo...

In this paper a method of embedding a linear graph in n-cube is discussed. Necessary and sufficient conditions on node configurations for the embeddability are obtained by analyzing the structure of n-cube in code space with respect to the distance 2c by means of Reed-Muller code. The fundamental idea in this study is to modify a given graph iteratively in such a manner that the connecting prop...

This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-ofthe-art word2vec model to embed a graph in Euclidean space via random walks on the nodes of the graph. In VEC-NBT, we modify the original algorithm to use a non-b...

We study provably effective and efficient data reduction for a class of NP-hard graph modification problems based on vertex degree properties. We show fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases while we show that there is no hope to achieve analogous results for the corresponding vertex or edge deletion versions. Our algorithms are based on transfor...