Related papers: The Reconstruction of Graphs
We present a new and powerful algebraic framework for graph rewriting, based on drags, a class of graphs enjoying a novel composition operator. Graphs are embellished with roots and sprouts, which can be wired together to form edges. Drags…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
Every finite graph $G$ can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like covering of $G$, whose tangle-tree structure is projected…
The tree of decomposition of a $k$-connected graph by a set $\mathfrak S$ of pairwise independent $k$-vertex cutsets is defined as follows. The vertices of this tree are cutsets of $\mathfrak S$ and parts of decomposition of the graph by…
In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to…
Verifying the veracity of claims requires reasoning over a large knowledge base, often in the form of corpora of trustworthy sources. A common approach consists in retrieving short portions of relevant text from the reference documents and…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
Model repair is an essential topic in model-driven engineering. Since models are suitably formalized as graph-like structures, we consider the problem of rule-based graph repair: Given a rule set and a graph constraint, try to construct a…
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…
Document structure analysis, such as zone segmentation and table recognition, is a complex problem in document processing and is an active area of research. The recent success of deep learning in solving various computer vision and machine…
In this article functorial Feynman rules are introduced as large generalizations of physicists Feynman rules, in the sense that they can be applied to arbitrary classes of hypergraphs, possibly endowed with any kind of structure on their…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random $d$-uniform hypergraph from its…
In this paper, we give a class of reconstructible graphs.
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…