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Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
There has been a surge of recent interest in learning representations for graph-structured data. Graph representation learning methods have generally fallen into three main categories, based on the availability of labeled data. The first,…
Graph databases are gaining momentum thanks to the flexibility and expressiveness of their data models and query languages. A standardization activity driven by the ISO/IEC standardization body is also ongoing and has already conducted to…
Graph labeling is a technique that assigns unique labels or weights to the vertices or edges of a graph, often used to analyze and solve various graph-related problems. There are few methods with certain limitations conducted by researchers…
An ultragraph gives rise to a labelled graph with some particular properties. In this paper we describe the algebras associated to such labelled graphs as groupoid algebras. More precisely, we show that the known groupoid algebra…
Graph and hypergraph representation learning has attracted increasing attention from various research fields. Despite the decent performance and fruitful applications of Graph Neural Networks (GNNs), Hypergraph Neural Networks (HGNNs), and…
Graph labeling problems have been widely studied in the last decades and have a vast area of application. In this work, we study the recently introduced S-labeling problem, in which the nodes get labeled using labels from 1 to |V | and for…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
We investigate Cayley graphs of finite semigroups and monoids. First, we look at semigroup digraphs, i.e., directed Cayley graphs of semigroups, and give a Sabidussi-type characterization in the case of monoids. We then correct a proof of…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
In recent years, the Graph Model has become increasingly popular, especially in the application domain of social networks. The model has been semantically augmented with properties and labels attached to the graph elements. It is difficult…
We consider a novel data driven approach for designing learning algorithms that can effectively learn with only a small number of labeled examples. This is crucial for modern machine learning applications where labels are scarce or…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…
We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often…