Related papers: Generating Functions For Kernels of Digraphs (Enum…
Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive…
Graph generation plays a pivotal role across numerous domains, including molecular design and knowledge graph construction. Although existing methods achieve considerable success in generating realistic graphs, their interpretability…
We present Digenes, a new discovery system that aims to help researchers in graph theory. While its main task is to find extremal graphs for a given (function of) invariants, it also provides some basic support in proof conception. This has…
Graph neural networks (GNNs), as a group of powerful tools for representation learning on irregular data, have manifested superiority in various downstream tasks. With unstructured texts represented as concept maps, GNNs can be exploited…
By using an approach of the invariant theory we obtain a new formula for the ordinary generating function of the numbers of the simple graphs with $n$ nodes.
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
Kernel methods are considered an effective technique for on-line learning. Many approaches have been developed for compactly representing the dual solution of a kernel method when the problem imposes memory constraints. However, in…
This paper presents Gem, a model-agnostic approach for providing interpretable explanations for any GNNs on various graph learning tasks. Specifically, we formulate the problem of providing explanations for the decisions of GNNs as a causal…
Functional brain graphs are often characterized with separate graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across brains and conditions. We anticipate that dense, weighted functional…
A directed graph $D=(V(D),A(D))$ has a kernel if there exists an independent set $K\subseteq V(D)$ such that every vertex $v\in V(D)-K$ has an ingoing arc $u\mathbin{\longrightarrow}v$ for some $u\in K$. There are directed graphs that do…
Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs…
Several algorithmic meta-theorems on kernelization have appeared in the last years, starting with the result of Bodlaender et al. [FOCS 2009] on graphs of bounded genus, then generalized by Fomin et al. [SODA 2010] to graphs excluding a…
Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis. Over the last two decades, numerous graph kernels, i.e. kernel functions…
In this paper, we fully answer the above question through a key algebraic condition on graph functions, called \textit{permutation compatibility}, that relates permutations of weights and features of the graph to functional constraints. We…
Graphs serve as fundamental descriptors for systems composed of interacting elements, capturing a wide array of data types, from molecular interactions to social networks and knowledge graphs. In this paper, we present an exhaustive review…
While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of…
Diffusion models achieve state-of-the-art performance in generating realistic objects and have been successfully applied to images, text, and videos. Recent work has shown that diffusion can also be defined on graphs, including graph…
Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. In…