Related papers: Multilevel Typed Graph Transformations
Heterogeneous graphs are ubiquitous in real-world applications because they can represent various relationships between different types of entities. Therefore, learning embeddings in such graphs is a critical problem in graph machine…
Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally…
A planar graph can be embedded in a piecewise linear manifold, and the lattice on each linear piece can be colored with 3-coloring. If a planar graph can be colored with multiple 3-coloring, i.e. coloring the graph in pieces with different…
We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite…
In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons…
Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…
We present two architectures for multi-task learning with neural sequence models. Our approach allows the relationships between different tasks to be learned dynamically, rather than using an ad-hoc pre-defined structure as in previous…
Graph-structured data consisting of objects (i.e., nodes) and relationships among objects (i.e., edges) are ubiquitous. Graph-level learning is a matter of studying a collection of graphs instead of a single graph. Traditional graph-level…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
Graph-structured data is prevalent in the real world. Recently, due to the powerful emergent capabilities, Large Language Models (LLMs) have shown promising performance in modeling graphs. The key to effectively applying LLMs on graphs is…
Recent advances in Vision-Language Models (VLMs) have shown promising capabilities in interpreting visualized graph data, offering a new perspective for graph-structured reasoning beyond traditional Graph Neural Networks (GNNs). However,…
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…
We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be…
This paper presents a complete classification of minimal graph surfaces that admit graphical transformations into other minimal surfaces. These transformations are functions that map the height function of a minimal graph surface to another…
We present a novel methodology to jointly perform multi-task learning and infer intrinsic relationship among tasks by an interpretable and sparse graph. Unlike existing multi-task learning methodologies, the graph structure is not assumed…
Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
A coloured graph is k-ultrahomogeneous if every isomorphism between two induced subgraphs of order at most k extends to an automorphism. A coloured graph is t-tuple regular if the number of vertices adjacent to every vertex in a set S of…