Related papers: A linear-time algorithm and analysis of graph Rela…
This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…
The Gromov-Hausdorff distance ($d_\mathrm{GH}$) provides a natural way of quantifying the dissimilarity between two given metric spaces. It is known that computing $d_\mathrm{GH}$ between two finite metric spaces is NP-hard, even in the…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
The classical Hausdorff dimension of finite or countable metric spaces is zero. Recently, we defined a variant, called \emph{finite Hausdorff dimension}, which is not necessarily trivial on finite metric spaces. In this paper we apply this…
For graph learning tasks, many existing methods utilize a message-passing mechanism where vertex features are updated iteratively by aggregation of neighbor information. This strategy provides an efficient means for graph features…
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…
In this paper we introduce and study discrete analogues of Lebesgue and Hausdorff dimensions for graphs. It turned out that they are closely related to well-known graph characteristics such as rank dimension and Prague (or…
In this thesis I propose an algorithm to heuristically calculate different distance measures on uncertain graphs (i.e. graphs where edges only exist with a certain probability) and apply this to the heuristic calculation of harmonic…
For a hereditary graph class $\mathcal{H}$, the $\mathcal{H}$-elimination distance of a graph $G$ is the minimum number of rounds needed to reduce $G$ to a member of $\mathcal{H}$ by removing one vertex from each connected component in each…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
We propose an efficient framework that integrates distance-aware multi-hop message passing with dynamic topology refinement. Unlike standard GNNs that rely on shallow, fixed-hop aggregation, DRTR leverages both static preprocessing and…
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
The Fr\'{e}chet distance is a well-studied similarity measure between curves that is widely used throughout computer science. Motivated by applications where curves stem from paths and walks on an underlying graph (such as a road network),…
We introduce a new distance measure for comparing polygonal chains: the $k$-Fr\'echet distance. As the name implies, it is closely related to the well-studied Fr\'echet distance but detects similarities between curves that resemble each…
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…