Related papers: Extending partial representations of function grap…
We study feature propagation on graph, an inference process involved in graph representation learning tasks. It's to spread the features over the whole graph to the $t$-th orders, thus to expand the end's features. The process has been…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a…
This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…
A cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and…
We study the problem of recognizing graph powers and computing roots of graphs. We provide a polynomial time recognition algorithm for r-th powers of graphs of girth at least 2r+3, thus improving a bound conjectured by Farzad et al. (STACS…
${ NP}$-complete problem "Hamiltonian cycle"\ for graph $G=(V,E)$ is extended to the "Hamiltonian Complement of the Graph"\ problem of finding the minimal cardinality set $H$ containing additional edges so that graph $G=(V,E\cup H)$ is…
A word-representable graph is a simple graph $G$ which can be represented by a word $w$ over the vertices of $G$ such that any two vertices are adjacent in $G$ if and only if they alternate in $w$. It is known that the class of…
We investigate the problem of training neural networks from incomplete images without replacing missing values. For this purpose, we first represent an image as a graph, in which missing pixels are entirely ignored. The graph image…
Activation functions are crucial in graph neural networks (GNNs) as they allow defining a nonlinear family of functions to capture the relationship between the input graph data and their representations. This paper proposes activation…
We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing…
We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
Social and information networks are gaining huge popularity recently due to their various applications. Knowledge representation through graphs in the form of nodes and edges should preserve as many characteristics of the original data as…
We study the planar orthogonal drawing style within the framework of partial representation extension. Let $(G,H,{\Gamma}_H )$ be a partial orthogonal drawing, i.e., G is a graph, $H\subseteq G$ is a subgraph and ${\Gamma}_H$ is a planar…
This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…