Related papers: A Note on the Modeling Power of Different Graph Ty…
Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
We study subclasses of grid intersection graphs from the perspective of order dimension. We show that partial orders of height two whose comparability graph is a grid intersection graph have order dimension at most four. Starting from this…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Argument graphs provide an abstract representation of an argumentative situation. A bipolar argument graph is a directed graph where each node denotes an argument, and each arc denotes the influence of one argument on another. Here we…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural…
Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty,…
Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive performance remains unclear. We introduce a family of premetrics that capture different degrees…
Dependencies between types in object-oriented software can be viewed as directed graphs, with types as nodes and dependencies as edges. The in-degree and out-degree distributions of such graphs have quite different forms, with the former…
The sum of the absolute values of the eigenvalues of a graph is called the energy of the graph. We study the problem of finding graphs with extremal energy within specified classes of graphs. We develop tools for treating such problems and…
Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the relation of the cardinalities of a maximum matching and the largest matching in those pairs. It is…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
In this work, we characterize the class of word-representable graphs with respect to the modular decomposition. Consequently, we determine the representation number of a word-representable graph in terms of the permutation-representation…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…