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In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
Over recent years there has been much interest in both Tur\'an and Ramsey properties of vertex ordered graphs. In this paper we initiate the study of embedding spanning structures into vertex ordered graphs. In particular, we introduce a…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
Let ${\cal G}=(G,w)$ be a weighted simple finite connected graph, that is, let $G$ be a simple finite connected graph endowed with a function $w$ from the set of the edges of $G$ to the set of real numbers. For any subgraph $G'$ of $G$, we…
How can we solve semi-supervised node classification in various graphs possibly with noisy features and structures? Graph neural networks (GNNs) have succeeded in many graph mining tasks, but their generalizability to various graph…
We investigate random connected graphs from a block-stable class whose distribution is weighted based on the number of $2$-connected components, or blocks. This includes the class of planar graphs. For this, we develop a notion of a…
Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
The problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting (perfect) matchings of some subgraph of an Aztec diamond graph A_n, or more generally calculating the sum of the weights…
The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with…
A graph $G=(V,E)$ is total weight $(k,k')$-choosable if the following holds: For any list assignment $L$ which assigns to each vertex $v$ a set $L(v)$ of $k$ real numbers, and assigns to each edge $e$ a set $L(e)$ of $k'$ real numbers,…
A network-theoretic approach for determining the complexity of a graph is proposed. This approach is based on the relationship between the linear algebra (theory of determinants) and the graph theory. In this paper we contribute a new…
For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The…
Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…
Integrated Gradients (IG) is a common explainability technique to address the black-box problem of neural networks. Integrated gradients assumes continuous data. Graphs are discrete structures making IG ill-suited to graphs. In this work,…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
Representing a label distribution as a one-hot vector is a common practice in training node classification models. However, the one-hot representation may not adequately reflect the semantic characteristics of a node in different classes,…
PAWS is a tool to analyse the behaviour of weighted automata and conditional transition systems. At its core PAWS is based on a generic implementation of algorithms for checking language equivalence in weighted automata and bisimulation in…