Related papers: Choosing Colors for Geometric Graphs via Color Spa…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
Modern graph embedding procedures can efficiently process graphs with millions of nodes. In this paper, we propose GEMSEC -- a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding.…
A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the…
Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper…
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…
The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss…
The classic greedy coloring (first-fit) algorithm considers the vertices of an input graph $G$ in a given order and assigns the first available color to each vertex $v$ in $G$. In the {\sc Grundy Coloring} problem, the task is to find an…
We investigate Fair and Tolerant (FAT) graph colorings, a coloring framework in which each vertex is allowed to share its color with a prescribed fraction of its neighbors, while the remaining neighbors are required to be distributed evenly…
Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a…
Region based knowledge graph embeddings represent relations as geometric regions. This has the advantage that the rules which are captured by the model are made explicit, making it straightforward to incorporate prior knowledge and to…
In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited…
The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that for all vertices v the color of v is different from the color of any of its neighbors. The problem is NP-hard.…
An edge labeling of a graph distinguishes neighbors by sets (multisets, resp.), if for any two adjacent vertices $u$ and $v$ the sets (multisets, resp.) of labels appearing on edges incident to $u$ and $v$ are different. In an analogous way…
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…
We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…