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Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their…
It is challenging for generative models to learn a distribution over graphs because of the lack of permutation invariance: nodes may be ordered arbitrarily across graphs, and standard graph alignment is combinatorial and notoriously…
Controlling network systems has become a problem of paramount importance. In this paper, we consider a distributed linear-quadratic problem and propose the use of graph neural networks (GNNs) to parametrize and design a distributed…
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
We consider graph Turing machines, a model of parallel computation on a graph, in which each vertex is only capable of performing one of a finite number of operations. This model of computation is a natural generalization of several…
We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
A new method for constructing self-referential tilings of Euclidean space from a graph directed iterated function system, based on a combinatorial structure we call a pre-tree, is introduced. In the special case that we refer to as…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Graph neural networks, a powerful deep learning tool to model graph-structured data, have demonstrated remarkable performance on numerous graph learning tasks. To address the data noise and data scarcity issues in deep graph learning, the…
We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the…
Computational intractability has for decades motivated the development of a plethora of methodologies that mainly aimed at a quality-time trade-off. The use of Machine Learning techniques has finally emerged as one of the possible tools to…
Recent advances in learning multi-modal representation have witnessed the success in biomedical domains. While established techniques enable handling multi-modal information, the challenges are posed when extended to various clinical…
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…