Related papers: Read networks and k-laminar graphs
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…
Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…
A graph is $k$-clique-extendible if there is an ordering of the vertices such that whenever two $k$-sized overlapping cliques $A$ and $B$ have $k-1$ common vertices, and these common vertices appear between the two vertices $a,b\in…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
Multi-hop machine reading comprehension is a challenging task in natural language processing as it requires more reasoning ability across multiple documents. Spectral models based on graph convolutional networks have shown good inferring…
Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node…
Recent literature posed the problem of characterising the graph degree sequences with exactly one $3$-polytopal (i.e. planar, $3$-connected) realisation. This seems to be a difficult problem in full generality. In this paper, we…
We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we…
k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it…
Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks.…
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…
Graph data is omnipresent and has a wide variety of applications, such as in natural science, social networks, or the semantic web. However, while being rich in information, graphs are often noisy and incomplete. As a result, graph…
A "book" with k pages consists of a straight line (the "spine") and k half-planes (the "pages"), such that the boundary of each page is the spine. If a graph is drawn on a book with k pages in such a way that the vertices lie on the spine,…
We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.
In this paper, we introduce the concept of $k$-integral graphs. A graph $\Gamma$ is called $k$-integral if the extension degree of the splitting field of the characteristic polynomial of $\Gamma$ over rational field $\mathbb Q$ is equal to…
Graph neural networks (GNNs) have evolved into one of the most popular deep learning architectures. However, GNNs suffer from over-smoothing node information and, therefore, struggle to solve tasks where global graph properties are…
We present a quantum algorithm solving the $k$-distinctness problem in $O(n^{1-2^{k-2}/(2^k-1)})$ queries with a bounded error. This improves the previous $O(n^{k/(k+1)})$-query algorithm by Ambainis. The construction uses a modified…
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…