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We present a semi-supervised learning framework based on graph embeddings. Given a graph between instances, we train an embedding for each instance to jointly predict the class label and the neighborhood context in the graph. We develop…
In this paper, we introduce tiled graphs as models of learning and maturing processes. We show how tiled graphs can combine graphs of learning spaces or antimatroids (partial hypercubes) and maturity models (total orders) to yield models of…
We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
In a semi-supervised learning scenario, (possibly noisy) partially observed labels are used as input to train a classifier, in order to assign labels to unclassified samples. In this paper, we study this classifier learning problem from a…
Graph neural networks (GNNs) achieve strong performance on homophilic graphs but often struggle under heterophily, where adjacent nodes frequently belong to different classes. We propose an interpretable and adaptive framework for…
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…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
Consider any locally checkable labeling problem $\Pi$ in rooted regular trees: there is a finite set of labels $\Sigma$, and for each label $x \in \Sigma$ we specify what are permitted label combinations of the children for an internal node…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and…
Graph-based methods have been demonstrated as one of the most effective approaches for semi-supervised learning, as they can exploit the connectivity patterns between labeled and unlabeled data samples to improve learning performance.…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph…
Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
In this study, we take a systematic look at the unrealised part of public transport networks (PTNs) with functional connections. We consider their complement graphs and study their structure. The complement graph $\bar G$ of an unweighted…
A method of classification of integrable equations on quad-graphs is discussed based on algebraic ideas. We assign a Lie ring to the equation and study the function describing the dimensions of linear spaces spanned by multiple commutators…